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1
Heylen, W., and T. Janter. "Extensions of the Modal Assurance Criterion." Journal of Vibration and Acoustics 112, no. 4 (October 1, 1990): 468–72. http://dx.doi.org/10.1115/1.2930130.
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The modal assurance criterion (MAC) in general measures the degree of proportion between two (modal) vectors, in the form of a correlation coefficient of a least squares ratio estimate. The MAC principle can be extended in several ways, thus increasing its field of applications. The partial MAC (PMAC) correlates parts of (modal) vectors. The spatial MAC (SMAC) allows to compare different vector spaces. Furthermore this paper suggests a way of calculating the MAC sensitivities to model changes. All those extensions are illustrated by their possible uses in correlating measured dynamic data with (finite element) matrix models and in the area of model updating. Those applications might be helpful tools to indicate regions of poor measurement-model correlation, to complete measured vectors, to judge approximate eigenvalue solvers, or to improve model updating procedures.
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Firoozbakht, Mehdi, Hamidreza Vosoughifar, and Alireza Ghari Ghoran. "Coverage intensity of optimal sensors for common, isolated, and integrated steel structures using novel approach of FEM-MAC-TTFD." International Journal of Distributed Sensor Networks 15, no. 8 (August 2019): 155014771985756. http://dx.doi.org/10.1177/1550147719857568.
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The coverage intensity of sensors is the most important issue on structural health monitoring technique. The geometric configuration of sensors must be optimized based on coverage intensity with proper objectives. In this article, a novel algorithm for optimal sensor placement in various steel frames was evaluated. These frames including moment-resisting frame, moment-resisting frame with base isolation, and moment-resisting frame with base isolation with steel shear wall were selected for case studies. This approach was proposed based on combination of common optimal sensor placement algorithm and nonlinear time history analysis. A new method called transformed time history to frequency domain approach was evaluated to transform nonlinear time history analysis results to frequency domain and then the effective frequencies according the maximum range of Fourier amplitude were selected. The modified type of modal assurance criterion values can be achieved from modal assurance criterion with the exact seismic displacement. All of novel optimal sensor placement processes were done through FEM-MAC-TTFD code modeled and developed in MATLAB by authors of this article. The results show that there is good relative correlation between the sensors number and coverage intensity obtained with modal and modified modal assurance criterion approaches for moment-resisting frame system, but for integrated frame such as moment-resisting frame with base isolation and moment-resisting frame with base isolation with steel shear wall, the modified modal assurance criterion approach is better approach. There is no significant difference between coverage intensity of sensors for top joints between modal assurance criterion and modified modal assurance criterion approaches for moment-resisting frame, moment-resisting frame with base isolation, and moment-resisting frame with base isolation with steel shear wall systems ( R2 = 0.994, 0.986, and 0.724, respectively). It was found that if reference point is located in center of frame, there is significant difference between modal assurance criterion and modified modal assurance criterion approaches, and modified modal assurance criterion generated slightly better results.
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Altunel, Fatih, Mehmet Çelik, and Mehmet Çalişkan. "A Correlation Improvement Technique for Model Updating of Structures." International Journal of Structural Stability and Dynamics 16, no. 08 (August 25, 2016): 1550049. http://dx.doi.org/10.1142/s0219455415500492.
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This study proposes a new correlation improvement technique for the optimum node removal location to get improved modal assurance criterion (MAC) matrix. The technique is applied to updating of the finite element model (FEM) of a structure. The developed routine is tried on a utility helicopter. It is proven that it is capable of showing better performance than the coordinate MAC (coMAC), commonly used in such analyses. Commercial software is utilized for the finite element analysis of the helicopter fuselage and tail. Experimental modal analyses are also performed for updating the model for tail of the helicopter to demonstrate the effectiveness of the new technique.
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Desforges, M. J., J. E. Cooper, and J. R. Wright. "Mode Tracking During Flutter Testing Using the Modal Assurance Criterion." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 210, no. 1 (January 1996): 27–37. http://dx.doi.org/10.1243/pime_proc_1996_210_342_02.
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Tracking the aeroelastic modes of an aircraft through changing flight conditions is an essential element of flight flutter testing, which is made difficult by corrupted data and high modal density. The modal assurance criterion (MAC), a method of evaluating the consistency of two modal vectors, is shown to simplify the mode tracking procedure by putting a numerical value on the correlation between pairs of modes identified at consecutive flight conditions. Representation of the resulting MAC values as a colour map gives a clear visual indication of modal consistency. An automated approach to mode tracking is introduced and shown to work on aircraft-type systems, over significant changes in flight condition up to and beyond the flutter speed. Some potential problems of a practical implementation are discussed.
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Xu, Yuanping, Jin Zhou, Long Di, Chen Zhao, and Qintao Guo. "Active Magnetic Bearing Rotor Model Updating Using Resonance and MAC Error." Shock and Vibration 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/263062.
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Modern control techniques can improve the performance and robustness of a rotor active magnetic bearing (AMB) system. Since those control methods usually rely on system models, it is important to obtain a precise rotor AMB analytical model. However, the interference fits and shrink effects of rotor AMB cause inaccuracy to the final system model. In this paper, an experiment based model updating method is proposed to improve the accuracy of the finite element (FE) model used in a rotor AMB system. Modelling error is minimized by applying a numerical optimization Nelder-Mead simplex algorithm to properly adjust FE model parameters. Both the error resonance frequencies and modal assurance criterion (MAC) values are minimized simultaneously to account for the rotor natural frequencies as well as for the mode shapes. Verification of the updated rotor model is performed by comparing the experimental and analytical frequency response. The close agreements demonstrate the effectiveness of the proposed model updating methodology.
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Yao, Dong Sheng, and Li Bin Zhao. "Scheme of Model Updating and Implement for Structural Dynamics Analysis." Applied Mechanics and Materials 252 (December 2012): 140–43. http://dx.doi.org/10.4028/www.scientific.net/amm.252.140.
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Model updating techniques are used to modify structural model for more accurate predictions of dynamics behavior. A simple survey on the model updating methods and correlation criteria is presented. Based on the inverse eigensensitivity method (IESM) and modal assurance criterion (MAC), a scheme of model updating for structures is presented and realized by user defined subroutine combined with APDL in commercial software ANSYS®. A four-DOF spring-mass system is assumed and updated, from which the predicted frequencies and MAC values are satisfied compared to the actual dynamics characteristics. This gives evidence that the presented model updating scheme is feasible and efficient. Furthermore, a cylindrical shell structure containing global and local modal information is established to research the updating ability of the scheme on some focused local modal information. The results due to the updated model of cylindrical shell structure show that not only the global modal data but also the local modal data have a good agreement with that of the actual structure.
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Samman, M. M. "A Modal Correlation Coefficient for Detection of Kinks in Mode Shapes." Journal of Vibration and Acoustics 118, no. 2 (April 1, 1996): 271–72. http://dx.doi.org/10.1115/1.2889658.
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A measure of correlation between mode shapes is introduced. This measure is a modification of the standard Modal Assurance Criterion (MAC). The new form, called the Modal Correlation Coefficient (MCC), is more sensitive to the existence of kinks in mode shapes. Its advantages are realized in diagnostic and structural health monitoring applications.
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Zhang, Rui, Zhen Fu Chen, Yuan Chu Gan, and Qiu Wang Tao. "Damage Diagnosis in Self-Compacting Concrete Beams Base on Eigenfrequencies and Mode Shape Derivatives." Applied Mechanics and Materials 160 (March 2012): 307–12. http://dx.doi.org/10.4028/www.scientific.net/amm.160.307.
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In this paper, modal characteristics of self-compacting concrete (SCC) beams were studied through experiment. 3 self-compacting concrete beams were gradually damaged and then subjected to vibration test in free-free boundary conditions after each load step. From analysis, eigenfrequencies could indicate the existence of damage but it could not represent the damage locations. Modal Assurance Criterion (MAC) is lesser reliable to indicate crack damage compare to eigenfrequencies. Next to these, capacity for damage detection and localization of Coordinate Modal Assurance Criterion (COMAC) and the flexibility matrix method are also examined and compared. This paper introduces in detail the dynamic properties and damage localization methods in SCC, which provide basal databases of damage diagnosis for SCC structures and promote the popularization of SCC in civil infrastructures.
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Zhan, Jie Zi, and Ling Yu. "Optimal Sensor Placement Based on Tabu Search Algorithms." Applied Mechanics and Materials 578-579 (July 2014): 1069–72. http://dx.doi.org/10.4028/www.scientific.net/amm.578-579.1069.
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In this study, the Tabu search (TS) algorithm is introduced into the optimal sensor placement (OSP) problem in the field of the structural health monitoring and moving force identification. A TS-based OSP procedure is proposed and further evaluated by some numerical simulations on a 2D planar truss model. The mean values of off-diagonal elements in a modal assurance criterion (MAC) matrix are used as the optimization objective function. Based on the criteria of MAC, determinant of fisher matrix, matrix condition number, and the least mean square error, the TS-based OSP procedure is evaluated through comparing with ones due to both of the energy coefficient-effective independence (ECEFI) and the effective independence (EFI) algorithms. The results show that the proposed TS-based OSP procedure is feasible with a higher accuracy.
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Khan, Mehran, Swarup Mahato, Darius Eidukynas, and Tomas Vaitkunas. "Influence determination of damage to mechanical structure based on modal analysis and modal assurance criterion." Vibroengineering PROCEDIA 42 (May 16, 2022): 27–32. http://dx.doi.org/10.21595/vp.2022.22554.
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Mechanical damages in structures changes its geometry in various ways. However, if damage size comparing to structure size is small, thus observation of this damage could be hard or even impossible in some cases. For this reason, changes in structure’s vibration responses are investigated nowadays. The objective of this research is to investigate the influence of damage size to the vibration response of the mechanical structure – aluminum alloy plate. To achieve this aim, modal analysis of a reference, i.e. health, and multiple damaged structures using ANSYS Workbench, and calculation of modal assurance criterion (MAC) using Matlab were carried out in this research. During this research 6 different damage sizes were modelled and its vibration response was compared to the health one. Obtained results revealed that the bending modes rarely shows any trend towards damages scenario. But, when observing the MAC values matrices, the values related to torsional modes even on the diagonal of the matrices decrease as the damage size increases, which indicates that the damage has more influence on the torsional modes.
11
Mas Colomer, Joan, Nathalie Bartoli, Thierry Lefebvre, and Joseph Morlier. "Aeroelastic scaling of flying demonstrators: mode tracking technique." Mechanics & Industry 23 (2022): 2. http://dx.doi.org/10.1051/meca/2021051.
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Aeroelastic scaling theory shows that the design problem of aeroelastically equivalent scaled aircraft can be treated as a structural-only design problem if the aerodynamic shape and airflow properties of the full scale aircraft are preserved. In that case, the theory shows that it is sufficient to match the scaled natural mode shapes, frequencies and mass of the reference aircraft. In this paper, we present a new method for the dynamic scaling of flexible structures where the objective function is based on the modal assurance criterion (MAC). This criterion is used for a mode tracking strategy during the optimization process. Finally, we apply this method to a scaled version (1:5) of the uCRM wing, achieving an agreement greater than 99% on the average MAC value of the first 5 modes.
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Zhang, Yunhe, Faping Zhang, Wuhong Wang, Fanjun Meng, Dashun Zhang, and Haixun Wang. "Prediction of Clearance Vibration for Intelligent Vehicles Motion Control." Sustainability 14, no. 11 (May 30, 2022): 6698. http://dx.doi.org/10.3390/su14116698.
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Motion control analysis should consider the system’s uncertainty to ensure the intelligent vehicle’s autonomy. The clearance structure of the transmission shaft is modeled as a cantilever beam with double clearance to predict the clearance vibration for mitigating the nonlinearity. Based on the Kelvin–Voigt collision model, a clearance model was developed using time-varying parameters identified by the wavelet transform. Comparing the frequency response functions (FRF) of the initial model with constant parameters and the updated model with time-varying parameters, the experimental results from the updated model indicate that the modal assurance criterion (MAC) is increased by 42.92%, 31.08%, 38.97%, and 50.74% in the first-four order. Cross-signature assurance criteria (CSAC) and cross-signature scale factor (CSF) have been increased by 6.55% and 12.37%. The control method based on the clearance model has been verified. In the case of 120 km/h, compared with model-predictive control (MPC) and sliding mode control (SMC), the peak of the lateral position error was reduced by 35.7% and 14.3%, and the peak of the heading error was reduced by 50% and 15.6%.
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Khiem, Nguyen Tien, and Phi Thi Hang. "A novel damage index extracted from frequency response of cracked Timoshenko beam subjected to moving harmonic load." Vietnam Journal of Mechanics 44, no. 3 (September 30, 2022): 280–91. http://dx.doi.org/10.15625/0866-7136/17546.
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In this paper, there is proposed a novel damage index extracted from frequency response of cracked Timoshenko beam under moving harmonic load using the so-called Modal Assurance Criterion (MAC) concept. First, frequency response of a cracked Timoshenko beam subjected to harmonic force moving on the beam with constant speed is obtained in an analytical expression. Then, a scalar characteristic like the coherence between the frequency responses of intact and cracked beams is determined and called herein Spectral Assurance Criterion (SAC). Such designed criterion is dependent upon crack parameters (location and depth), the load frequency and speed as well as position on beam where the responses have been measured. Numerical analysis shows that SAC is much more sensitive to crack than natural frequencies and can be used as a novel damage index for crack detection in beam using moving load. The effect of moving load frequency and speed has been also examined with the aim to have got an indicator most adequate for the crack detection problem.
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Chen, Yu Jing, Min Zhang, Yuan Dong Meng, Qiang Zhao, and Jie Wen Nie. "Modal Parameter Identification of Jacket-Type Platforms Using Vibration Testing Data." Applied Mechanics and Materials 170-173 (May 2012): 2243–47. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.2243.
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How to estimate the modal parameters (including natural frequencies and mode shapes) of an offshore platform accurately is crucial for the health monitoring problems. The purpose of this paper is to identify the modal parameters of a physical jacket-type platform model from measured modal testing data using Prony’s method. In the modal testing, the identified false modes are unavoidable and bring much difficulty to determine the accurate modal parameters. To solve these problems, in this paper, the Modal Phase Collinearity (MPC) and Modal Assurance Criterion (MAC) are applied to distinguish the true and false modal. The measured data are extracted from a physical model of a realistic offshore platform. And the results demonstrate that the modal parameters of the first two modes of each direction can be accurately estimated by using the proposed method.
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Jarosińska, Małgorzata, and Stefan Berczyński. "Changes in Frequency and Mode Shapes Due to Damage in Steel–Concrete Composite Beam." Materials 14, no. 21 (October 20, 2021): 6232. http://dx.doi.org/10.3390/ma14216232.
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This study presents an analysis of changes in the vibration frequency and mode of vibration of a composite beam due to damage. A steel–concrete composite beam was considered, for which numerical analysis (RFE model) and experimental tests were conducted. Two levels of damage were introduced to the beam. To determine the changes in the mode of vibration before and after the damage, the modal assurance criterion (MAC) and its partial variation (PMAC) were applied. The curvature damage factor (CDF) was used to determine the changes in the modal curvature. The natural frequencies were sensitive to the introduced damage. The results show that the MAC is not effective in determining the location of damage in the connection plane. Two different coefficients were introduced to locate the damage. The PMAC was used for sections of subsequent modes of vibration and allowed effectively locating the damage. The CDF considered simultaneous changes in the curvatures of all vibration modes and was effective in locating the damage in the connection plane.
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Nguyen, Minh, Angelos Filippatos, Albert Langkamp, and Maik Gude. "Modal Identification of Output-Only Systems of Composite Discs Using Zernike Modes and MAC." Sensors 19, no. 3 (February 6, 2019): 660. http://dx.doi.org/10.3390/s19030660.
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The analysis of the structural dynamic behaviour of composite rotor–discs by a valid description of the eigenfrequencies and mode shapes can provide significant information for action-taking before a failure occurs. Specifically, vibration-based diagnostic methods, which are able to take into consideration the interdependencies and sequential changes of the modal properties could benefit from such an analysis. Here, on the example of composite rotors, a correlation method for experimentally determined mode shapes is developed. For this purpose the Zernike polynomials are used to enhance the identification of mode shapes. Furthermore, the modal assurance criterion (MAC) in combination with the frequency response criterion and a data processing approach are applied in order to characterize changing modal properties of composite rotors. In addition, the developed algorithms can be further extended in order to simplify the experimental evaluation of the complex dynamic behaviour of composite structures.
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Patuelli, Cesare, Enrico Cestino, and Giacomo Frulla. "A Beam Finite Element for Static and Dynamic Analysis of Composite and Stiffened Structures with Bending-Torsion Coupling." Aerospace 10, no. 2 (February 3, 2023): 142. http://dx.doi.org/10.3390/aerospace10020142.
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This research presents a new beam finite element capable of predicting static and dynamic behavior of beam structures with bending-torsion coupling. The model here derived establishes a relation between the bending and torsional nodal degree of freedom of a two node beam element. The equilibrium equations are derived neglecting the non-linear terms while the stiffness and mass matrices are derived with Galerkin’s method. The shape functions are obtained considering Timoshenko’s hypothesis and the torsional moment constant along the element. The model has been validated through numerical and experimental results for static and dynamic simulation. The comparison revealed a relative difference mostly lower than 5% for static deformations and natural frequency prediction, while the Modal Assurance Criterion (MAC) confirmed the consistency with numerical and experimental results in terms of mode shape similarity.
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Bianconi, Francesca, Georgios Panagiotis Salachoris, Francesco Clementi, and Stefano Lenci. "A Genetic Algorithm Procedure for the Automatic Updating of FEM Based on Ambient Vibration Tests." Sensors 20, no. 11 (June 10, 2020): 3315. http://dx.doi.org/10.3390/s20113315.
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The dynamic identification of the modal parameters of a structure, in order to gain control of its functionality under operating conditions, is currently under discussion from a scientific and technical point of views. The experimental observations obtained through structural health monitoring (SHM) are a useful calibration reference of numerical models (NMs). In this paper, the procedures for the identification of modal parameters in historical bell towers using a stochastic subspace identification (SSI) algorithm are presented. Then, NMs are manually calibrated on the identification’s results. Finally, the applicability of a genetic algorithm for the automatic calibration of the elastic parameters is considered with the aim of searching for the properties of the autochthonous material, in order to reduce modelling error following the model assurance criterion (MAC). In this regard, several material values on the same model are examined to see how to approach the evolution and the distribution of these features, comparing the characterization proposed by the genetic algorithm with the results considered by the manual iterative procedure.
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Lee, Eun-Taik, and Hee-Chang Eun. "An Optimal Sensor Layout Using the Frequency Response Function Data within a Wide Range of Frequencies." Sensors 22, no. 10 (May 16, 2022): 3778. http://dx.doi.org/10.3390/s22103778.
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This study presents iterative optimal sensor placement (OSP) techniques using the modal assurance criterion (MAC) and the effective independence (EI) algorithm. The algorithms use the proper orthogonal mode (POM) extracted from the frequency response functions (FRFs) of dynamic systems within a wide range of frequencies. The FRF-based OSP method proposed in this study has the merit of reflecting dynamic characteristics, unlike the mode shape-based method. Evaluating the MAC values and the EI indices at each iteration, the DOFs of low contribution to the objective function of candidate sensor DOFs are deleted from master DOFs and moved to slave DOFs. This process is repeated until the sensor number corresponds with the master DOFs. The validity of the proposed methods is illustrated in an example, the sensor layouts by the proposed methods are compared, and the layout inconsistency between the MAC and the EI techniques is analyzed.
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Zhang, Wei Dong, Jun Wan, Yi Bo Ai, and Bin Yang. "An Acceleration Sensor Placement Method Considering Network Life Cycle for Vibration Monitoring of Bridges." Applied Mechanics and Materials 361-363 (August 2013): 1264–71. http://dx.doi.org/10.4028/www.scientific.net/amm.361-363.1264.
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Vibration is a very important signal for the health monitoring of bridge. Wireless sensor network powered by batteries are widely used in the monitoring system. How to prolong the network life cycle becomes an important problem due to the limitation of battery energy. This paper presents a new method of optimal acceleration sensor placement for monitoring the vibration of bridges, the method considers network life cycle as the second target on the basis of traditional modal assurance criterion (MAC). And multiple-objective optimization is performed by using a genetic algorithm. The simulation result shows that when the sensors number is less than 30, the networks life cycle can be greatly extended with the addition of only the little cost of MAC indicators.
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Fadhil Shazmir, M., N. Ayuni Safari, M. Azhan Anuar, A. A.Mat Isa, and Zamri A.R. "Operational Modal Analysis on a 3D Scaled Model of a 3-Storey Aluminium Structure." International Journal of Engineering & Technology 7, no. 4.27 (November 30, 2018): 78. http://dx.doi.org/10.14419/ijet.v7i4.27.22485.
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Obtaining a good experimental modal data is essential in modal analysis in order to ensure accurate extraction of modal parameters. The parameters are compared with other extraction methods to ascertain its consistency and validity. This paper demonstrates the extraction of modal parameters using various identification algorithms in Operational Modal Analysis (OMA) on a 3D scaled model of a 3-storey aluminium structure. Algorithms such as Frequency Domain Decomposition (FDD), Enhanced Frequency Domain Decomposition (EFDD) and Stochastic Subspace Identification (SSI) are applied in this study to obtain modal parameters. The model test structure is fabricated of aluminium and assembled using bolts and nuts. Accelerometers were used to collect the responses and the commercial post processing software was used to obtain the modal parameters. The resulting natural frequencies and mode shapes using FDD method are then compared with other OMA parametric technique such as EFDD and SSI algorithm by comparing the natural frequencies and Modal Assurance Criterion (MAC). Comparison of these techniques will be shown to justify the validity of each technique used and hence confirming the accuracy of the measurement taken.
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Shao, Huajin, Yanfei Zuo, and Zhinong Jiang. "Dynamic Finite Element Model Updating Based on Correlated Mode Auto-Pairing and Adaptive Evolution Screening." Applied Sciences 12, no. 6 (March 20, 2022): 3175. http://dx.doi.org/10.3390/app12063175.
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A method for dynamic finite element (FE) model updating based on correlated mode auto-pairing and adaptive evolution screening (CMPES) is proposed to overcome difficulties in pairing inaccurate analytical modal data and incomplete experimental modal data. In each generation, the correlated mode pairings (CMPs) are determined by modal assurance criterion (MAC) values and the symbiotic natural frequency errors, according to an auto-pairing strategy. The objective function values constructed by correlated and penalized subitems are calculated to screen the better individuals. Then, both the updating parameters and the CMPs can be adjusted adaptively to simultaneously approach the ideal results during the iteration of population evolution screening. Three examples (a thin plate with small holes, an F-shaped structure, and an intermediate case with multi-layer thin-walled complex structure) were presented to validate the accuracy, effectiveness, and engineering application potential of the proposed method.
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Markiewicz, Barbara, Grzegorz Piątkowski, Łukasz Szyszka, and Dominika Ziaja. "Experimental verification of the numerical model of a reinforced concrete arch." MATEC Web of Conferences 285 (2019): 00010. http://dx.doi.org/10.1051/matecconf/201928500010.
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The paper presents numerical and experimental dynamic analysis of the reinforced concrete arch. The measurement of the accelerations at various points of the structure as a response to the force (single input-multiple output approach) was made. Dynamic response of the concrete arch has been measured by piezoelectric accelerometers and signals have been recorded by multi-channel LMS SCADAS Mobile recorder. As a result of the measurements frequencies and mode shapes have been determined. ADINA program has been used for building of numerical models. The static scheme of the arch (the stiffness of the supports) has been updated using the genetic algorithms (GA) available in MATLAB to obtain the results, which correspond to dynamic testing. Two similarity criteria have been considered: the mean squared error (MSE) between frequencies and the Modal Assurance Criterion (MAC) for forms comparison. In additional example, the Young’s modulus has been also optimized.
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Jull, Martin Ø. Ø., Sandro D. R. Amador, Anders Skafte, Jannick B. Hansen, Manuel L. Aenlle, and Rune Brincker. "One-Step FE Model Updating Using Local Correspondence and Mode Shape Orthogonality." Shock and Vibration 2019 (January 2, 2019): 1–12. http://dx.doi.org/10.1155/2019/1362954.
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In this paper, it is described how the matrix mixing model updating technique can be combined with the local correspondence (LC) mode shape expansion algorithm, to give a new finite element (FE) model updating method. The matrix mixing method uses that the inverse mass and stiffness matrices can be expressed as a linear combination of outer products of FE mode shape vectors, where the low-frequency part of these sums are substituted with expanded test modes. The approach is meant to update FE models in one-step and is exact, except for the following two approximations: the mode shape smoothing and the mass scaling of the expanded experimental mode shapes. A simulation study illustrates the errors from the two approximations and shows the ability of the technique to improve the modal assurance criterion (MAC) values so that they get very close to unity. Finally, the performance of the proposed updating method is assessed by means of an application example in which the FE model is updated based on the test modes of a real structure.
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Drygała, Izabela, Joanna M. Dulinska, and Marek Wazowski. "Assessment of human-induced vibrations of a cable-stayed footbridge." MATEC Web of Conferences 211 (2018): 09001. http://dx.doi.org/10.1051/matecconf/201821109001.
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The primary purpose of this research is the evaluation of human-induced vibrations of a cable-stayed footbridge. The cable-stayed pedestrian bridge with total length of the span equal to 46.90 m located in Czestochowa (Southern Poland) was chosen as a case study. The footbridge consists of two spans (21.10 m and 25.80 m). A three-dimensional (3D) finite element (FE) model of the footbridge was prepared with the ABAQUS software program. The dynamic properties of the structure, i.e. its natural frequencies, modes shapes and damping ratios, were estimated on the basis of the in situ tests results as well as numerical analysis. For the validation of the modal models the modal assurance criterion (MAC) theory was applied. In the next stage of the investigation the dynamic response of the structure to human-induced loading was evaluated. Finally, the vibration comfort criteria for the footbridge were checked.
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Zhou, Chuandi, Yibing Liu, Ji Wu, and Chao Zhou. "Optimal Sensor Placement and Minimum Number Selection of Sensors for Health Monitoring of Transmission Towers." Shock and Vibration 2020 (December 28, 2020): 1–12. http://dx.doi.org/10.1155/2020/2375947.
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Transmission towers are structurally complex, which makes it challenging to choose the right place and number of sensors for health monitoring. In this paper, optimal sensor placement of a cat-head-type transmission tower is conducted by using the Effective Independent Method (EIM) and a method is proposed for calculating the minimum number of sensors for structural health monitoring by combining EIM and Modal Assurance Criterion (MAC). The method for calculating the number of sensors prescribed in this paper derives a curve that shows the relationship between MAC value and the number of sensors. It is found that the MAC value decreases with increase in the number of sensors. When the number of sensors reaches a certain threshold, the curve tends to stabilize. Then, the number of sensors corresponding to the minimum MAC is proposed as the minimum number of sensors. Through calculation, the minimum number of sensors of the cat-head-type transmission tower is obtained. Also, the optimal sensor placement results show that the position of a large number of sensors includes the position of a smaller number of sensors.
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Lin, Chang-Sheng, and Ming-Hsien Lin. "Output-Only Modal Estimation Using Eigensystem Realization Algorithm with Nonstationary Data Correlation." Applied Sciences 11, no. 7 (March 30, 2021): 3088. http://dx.doi.org/10.3390/app11073088.
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The conventional eigensystem realization algorithm with data correlation (ERA/DC) combines the impulse response or free response data of a structural system with the concept of correlation function to identify the modal parameter of the structural system. Previous studies have shown that the modal parameters of structural systems subjected to stationary white noise excitation can be estimated by ERA/DC from the ambient response without excitation data. This concept is extended in this paper for output-only modal identification for the structural system with complex modes under ambient excitation as a nonstationary process in the form of a product model. Numerical simulations and experimental verification are used to validate the effectiveness of the proposed method for response-only modal estimation, and the stabilization diagram is used with modal assurance criterion (MAC) to distinguish structural modes from fictitious modes.
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Hryciów, Zdzisław, Jerzy Małachowski, Piotr Rybak, and Andrzej Wiśniewski. "Research of Vibrations of an Armoured Personnel Carrier Hull with FE Implementation." Materials 14, no. 22 (November 11, 2021): 6807. http://dx.doi.org/10.3390/ma14226807.
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Modern wheeled armoured vehicles can perform a variety of tasks, making the development of weapon systems that can be safely and effectively integrated with the vehicle structure an area of interest. Due to the cost of implementing new models, it is more economical to test potential configurations using numerical methods, such as the finite element method. The numerical model has been validated to confirm the reliability of the obtained results. Modal tests were also performed using four configurations to identify the frequency and mode shape of natural vibrations occurring within the support structure. In an experimental setting, hull vibrations were forced using the modal hammer testing method. The modal assurance criterion (MAC) and the authors’ procedure were used to confirm the experimental and numerical test results. Additional testing in the form of impact loads was carried out for turret-containing structures. Structural strain at indicated points and forces transmitted by brackets to the bottom of the hull were compared.
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Chen, Xi, and Ling Yu. "Flexibility-Based Objective Functions for Constrained Optimization Problems on Structural Damage Detection." Advanced Materials Research 186 (January 2011): 383–87. http://dx.doi.org/10.4028/www.scientific.net/amr.186.383.
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Based on concepts of structural modal flexibility and modal assurance criterion (MAC), a new objective function is defined and studied for constrained optimization problems (COP) on structural damage detection (SDD) in this paper. Compared with traditionally objective function, which is defined based on natural frequencies and MAC, effect of objective functions on robustness of SDD calculation is evaluated through numerical simulation of a 2-storey rigid frame. Structural damages are identified by solving the COP on SDD based on an improved particle swarm optimization (IPSO) algorithm. Weak and multiple damage scenarios are mainly considered in various noise conditions. Some illustrated results show that the newly defined objective function is better than the traditional ones. It can be used to identify the damage locations but also to quantify the severity of weak and multiple damages in measurement noise conditions.
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Ribeiro, Diogo, Cássio Bragança, Maik Brehm, Volkmar Zabel, and Rui Calçada. "A Novel Strategy for Automatic Mode Pairing on the Model Updating of Railway Systems with Nonproportional Damping." Applied Sciences 13, no. 1 (December 27, 2022): 350. http://dx.doi.org/10.3390/app13010350.
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Mode pairing is a crucial step for the stability of any model-updating strategy based on experimental modal parameters. Automatically establishing a stable and assertive correspondence between numerical and experimental modes, in many cases, proves to be a very challenging task, especially in situations where complex mode shapes are present. This article presents a novel formulation for the automatic mode pairing between experimental and numerical complex modes based on an Energy-based Modal Assurance Criterion (EMAC). The efficiency of the proposed criterion was demonstrated on the basis of a case study involving the pairing between numerical and experimental modes of a passenger railway vehicle. A highly complex detailed FE numerical model of the vehicle was developed involving the modeling of the carbody, bogies and axles. A numerical damped modal analysis allowed obtaining the main global rigid-body and flexural modes of the vehicle’s carbody, as well as several local modes associated to the vibration of specific components of the carbody. Due to the localized damping provided by the suspensions, these modes presented complex modal ordinates, especially for the rigid-body modes. The comparison between the results obtained from the application of the EMAC and the classical MAC criteria, on the pairing of five global mode shapes, proved that the EMAC criterion is much more assertive, avoiding mismatches between the experimental global modes and some of the local numerical modes with similar configurations, and, consequently, establishing the correct correspondences between experimental and numerical modes.
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Fu, Yong Ming, and Ling Yu. "Optimal Sensor Placement Based on MAC and SPGA Algorithms." Advanced Materials Research 594-597 (November 2012): 1118–22. http://dx.doi.org/10.4028/www.scientific.net/amr.594-597.1118.
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In order to solve the problem on sensor optimization placement in the structural health monitoring (SHM) field, a new sensor optimization method is proposed based on the modal assurance criterion (MAC) and the single parenthood genetic algorithm (SPGA). First, the required sensor numbers are obtained by using the step accumulating method. The SPGA is used to place sensors, in which the binary coding is adopted to realize the genetic manipulation through gene exchange, gene shift and gene inversion. Then, the method is further simplified and improved for higher computation efficiency. Where, neither the individual diversity of initial population nor the immature convergence problem is required. Finally, a numerical example of 61 truss frame structure is used to assess the robustness of the proposed method. The illustrated results show that the new method is better than the improved genetic algorithm and the step accumulating method in the search capacity, computational efficiency and reliability.
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Zhan, Jie Zi, and Ling Yu. "An Effective Independence-Improved Modal Strain Energy Method for Optimal Sensor Placement of Bridge Structures." Applied Mechanics and Materials 670-671 (October 2014): 1252–55. http://dx.doi.org/10.4028/www.scientific.net/amm.670-671.1252.
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In this study, an effective independence-improved modal strain energy (EI-IMSE) method is proposed for the optimal sensor placement (OSP) problem in the field of the structural health monitoring and moving force identification. The improved modal strain energy (IMSE) is used to modify optimal sensor placement results obtained by the effective independence (EI) method. The EI-IMSE OSP method is verified by some numerical simulations on a 2D planar truss bridge model. Based on the criteria of modal assurance criterion (MAC), trace of fisher matrix, matrix condition number, and the least mean square error, the EI-IMSE OSP method is assessed through comparing with those of EI, EI-driving point residue (EI-DPR), EI-average driving DOF velocity (EI-ADDOFV), and EI-average acceleration amplitude (EI-AAA). The illustrated results show that the proposed EI-IMSE OSP method is feasible with a higher accuracy.
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Zhang, Li, Su Bin, Feng Tao, Ye Tian, and Jiang Yue Peng. "Experimental Modal Analysis of the Industrial Flat Sewing Machine Based on PolyMax Algorithm." Advanced Materials Research 744 (August 2013): 137–42. http://dx.doi.org/10.4028/www.scientific.net/amr.744.137.
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In this paper, the free modal of the industrial flat sewing machine was researched, and the experimental measurement system is established. A modal analysis of industrial flat sewing machine is carried out through the method of single point exciting vibration and multipoint collecting signal. The PolyMax modal parameter identification method is applied to the modal analysis for frequency response function to get steady state diagram and then determine the modal parameters and modal shapes. According to Modal Assurance Criterion (MAC), the credibility of the calculation results is verified, and then modal parameters of industrial flat sewing machine get more reliable in order to provide the reference for further structure optimization and noise reduction of the flat sewing machine.
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Alpaslan, Emre. "Investigation on Similarity between Dynamic Behavior of a Reduced-Scale One Span Historical Masonry Arch Bridge Model and Prototype Bridge." Civil Engineering Beyond Limits 1, no. 1 (December 17, 2019): 5–11. http://dx.doi.org/10.36937/cebel.2020.001.002.
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Experimental investigations of large and complex structural systems can be carried out by reduced-scale models in terms of convenience, time-saving and economical. This can be applied to different fields of study such as vibration, impact and explosion problems in structural engineering and allows reliable analysis to understand the static and dynamic behavior of real structures called a prototype. This study aims that a 1/3 reduced-scale model is created in the laboratory environment considering similitude requirements by selecting a single span historical masonry arch bridge as a prototype structure. For this purpose, the Operational Modal Analysis (OMA) Technique is utilized for experimental study to determine modal parameters of the prototype and model bridges. The similarity of the dynamic behavior of the reduced-scale bridge model and prototype are investigated. The analysis of the similarity in the dynamic behavior of the prototype and model bridge consists of comparing the natural frequencies and mode shapes by utilizing the modal assurance criterion (MAC) corresponding to the translational, bending and torsional modes. As a result of the study, it is concluded that the dynamic behavior of the reduced-scale bridge model is similar to the dynamic behavior of the prototype bridge.
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Kim, Chan-Jung. "Mode Tracking of Unidirectional Carbon-Based Composite Structures Using Modified Mode Shape Vectors." Crystals 12, no. 2 (February 9, 2022): 236. http://dx.doi.org/10.3390/cryst12020236.
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A comparison of mode shapes in isotropic structures can be efficiently performed using the modal assurance criterion (MAC) to determine the similarity between mode shape vectors. However, the unidirectional, carbon-based composite (UCBC) structure shows different dynamic characteristics according to the carbon fiber orientation, even for the same structural configuration. The MAC of a certain mode may result in a poor value for the CBC structures in the case of the existence of the distorted mode shape vector from reinforced carbon fibers. In this study, the mode tracking of the UCBC structure is proposed using the MAC value only under the modified mode shape vector to enhance the MAC value between relevant modes. Because the mode shape vectors of the UCBC structure are altered from those of the isotropic structure owing to the reinforced stiffness along the carbon fiber orientation, the modified mode shape vectors are calculated by multiplying the original vectors with the proposed modification window. The proposed method was verified for simple UCBC structures with five different carbon fiber orientations, from 0° to 90°. The UCBC structures were tracked for five modes, three bending and two torsional, and the results were discussed with reference to earlier study results.
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Zhang, Weiguo, and Octavian Postolache. "Parametric model updating with frequency and MAC combined objective function of port crane structure based on operational modal analysis." Open Physics 17, no. 1 (March 28, 2019): 69–76. http://dx.doi.org/10.1515/phys-2019-0008.
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Abstract In FE modeling of port crane structures, errors may be caused due to the simplification of complicated components, unclear physical properties, local approximation and inaccurate boundary conditions. So it is very important to update the FE model accuracy according to the experiment model and results. However there are two major problems when solving the model updating of port crane structure, the one is the difficulty of collecting the structure modal parameters with traditional modal experiment method because of the large scale of port crane structure, the other is mismatching problem while updating processing due to most of the model updating method currently constructing the objective function only by frequency. In this paper, an operational modal analysis is adopted to estimate the modal parameters of port crane structure based on the operational condition. A parametric model updating methodology of finite element (FE) model is proposed to solve port crane structure model updating: a series of design parameters of the FE model of port crane structure are selected as the main factors based on the sensitivity analysis, the objective function is built by considering the frequency correlation and the modal assurance criterion (MAC) together, and finally a zero-order/first-order combination algorithm is utilized to get the final accurate FE model of port crane structure. Research results showed that methodology proposed in this paper has satisfied updating accuracy for port crane structure, which verifies that the proposed method is suitable for model updating problem of this kind of structure.
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Rotondella, Vincenzo, Andrea Merulla, Andrea Baldini, and Sara Mantovani. "Dynamic Modal Correlation of an Automotive Rear Subframe, with Particular Reference to the Modelling of Welded Joints." Advances in Acoustics and Vibration 2017 (April 3, 2017): 1–9. http://dx.doi.org/10.1155/2017/8572674.
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This paper presents a comparison between the experimental investigation and the Finite Element (FE) modal analysis of an automotive rear subframe. A modal correlation between the experimental data and the forecasts is performed. The present numerical model constitutes a predictive methodology able to forecast the experimental dynamic behaviour of the structure. The actual structure is excited with impact hammers and the modal response of the subframe is collected and evaluated by the PolyMAX algorithm. Both the FE model and the structural performance of the subframe are defined according to the Ferrari S.p.A. internal regulations. In addition, a novel modelling technique for welded joints is proposed that represents an extension of ACM2 approach, formulated for spot weld joints in dynamic analysis. Therefore, the Modal Assurance Criterion (MAC) is considered the optimal comparison index for the numerical-experimental correlation. In conclusion, a good numerical-experimental agreement from 50 Hz up to 500 Hz has been achieved by monitoring various dynamic parameters such as the natural frequencies, the mode shapes, and frequency response functions (FRFs) of the structure that represent a validation of this FE model for structural dynamic applications.
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Le, Vinh Tung, and Nam Seo Goo. "Dynamic Characteristics and Damage Detection of a Metallic Thermal Protection System Panel Using a Three-Dimensional Point Tracking Method and a Modal Assurance Criterion." Sensors 20, no. 24 (December 15, 2020): 7185. http://dx.doi.org/10.3390/s20247185.
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A thermal protection system (TPS) is designed and fabricated to protect a hypersonic vehicle from extreme conditions. Good condition of the TPS panels is necessary for the next flight mission. A loose bolted joint is a crucial defect in a metallic TPS panel. This study introduces an experimental method to investigate the dynamic characteristics and state of health of a metallic TPS panel through an operational modal analysis (OMA). Experimental investigations were implemented under free-free supports to account for a healthy state, the insulation effect, and fastener failures. The dynamic deformations resulted from an impulse force were measured using a non-contact three-dimensional point tracking (3DPT) method. Using changes in natural frequencies, the damping ratio, and operational deflection shapes (ODSs) due to the TPS failure, we were able to detect loose bolted joints. Moreover, we also developed an in-house program based on a modal assurance criterion (MAC) to detect the state of damage of test structures. In a damage state, such as a loose bolted joint, the stiffness of the TPS panel was reduced, which resulted in changes in the natural frequency and the damping ratio. The calculated MAC values were less than one, which pointed out possible damage in the test TPS panels. Our results also demonstrated that a combination of the 3DPT-based OMA method and the MAC achieved good robustness and sufficient accuracy in damage identification for complex aerospace structures such as TPS structures.
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Pitarresi, J. M., D. V. Caletka, R. Caldwell, and D. E. Smith. "The “Smeared” Property Technique for the FE Vibration Analysis of Printed Circuit Cards." Journal of Electronic Packaging 113, no. 3 (September 1, 1991): 250–57. http://dx.doi.org/10.1115/1.2905403.
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The primary objective of this paper is to investigate the accuracy of the finite element (FE) smeared properties approach for the determination of the mode shapes and frequencies of a printed wiring board (PWB) populated with electronic modules. Smearing of the material and/or structural properties is a recognized means of reducing a complicated structure to a less complicated approximation. Comparisons of both the natural frequencies and mode shapes are made between the smeared FE model and those obtained from vibration testing. The extent of correlation between the mode shapes is characterized by the modal assurance criterion (MAC). Since the intent of this study is to examine the effectiveness of the smearing technique, free boundary conditions are assumed. It is shown that the smearing technique can produce good correlation of both natural frequencies and mode shapes of PWBs populated with modules. A case study of a PWB with both surface mount technology (SMT) and pin-in-hole (PIH) components is presented.
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Zang, C., H. B. Lan, D. D. Jiang, and M. I. Friswell. "Mode Shape Description and Model Updating of Axisymmetric Structures Using Radial Tchebichef Moment Descriptors." Shock and Vibration 2021 (March 9, 2021): 1–19. http://dx.doi.org/10.1155/2021/8895583.
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A novel approach for mode shape feature extraction and model updating of axisymmetric structures based on radial Tchebichef moment (RTM) descriptors is proposed in this study. The mode shape features extracted by RTM descriptors can effectively compress the full-field modal vibration data and retain the most important information. The reconstruction of mode shapes using RTM descriptors can accurately describe the mode shapes, and the simulation shows that the RTM function is superior to Zernike moment function in terms of its mathematical properties and its shape reconstruction ability. In addition, the proposed modal correlation coefficient of the RTM amplitude can overcome the main disadvantage of using the modal assurance criterion (MAC), which has difficulty in identifying double or close modes of symmetric structures. Furthermore, the model updating of axisymmetric structures based on RTM descriptors appears to be more efficient and effective than the normal model updating method directly using modal vibration data, avoids manipulating large amounts of mode shape data, and speeds up the convergence of updating parameters. The RTM descriptors used in correlation analysis and model updating are demonstrated with a cover of an aeroengine rig. The frequency deviation between the test and the FE model was reduced from 17.13% to 1.23% for the first 13 modes via the model updating process. It verified the potential to industrial application with the proposed method.
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Zhang, Xing, Wei Li, Zhencai Zhu, Shanguo Yang, and Fan Jiang. "Fault Detection for the Scraper Chain Based on Vibration Analysis Using the Adaptive Optimal Kernel Time-Frequency Representation." Shock and Vibration 2019 (July 24, 2019): 1–14. http://dx.doi.org/10.1155/2019/6986240.
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A scraper conveyor is a key component of large-scale mechanized coal mining equipment, and its failure patterns are mainly caused by chain jam and chain fracture. Due to the difficulties with direct measurement for multiple performance parameters of the scraper chain, this paper deals with a novel strategy for fault detection of the scraper chain based on vibration analysis of the chute. First, a chute vibration model (CVM) is applied for modal analysis, and the hammer impact test (HIT) is conducted to validate the accuracy of the CVM; second, the measuring points for vibration analysis of the chute are determined based on the modal assurance criterion (MAC); and third, to simulate the actual vibration properties of the chute, a dynamic transmission system model (DTSM) is constructed based on finite element modeling. The fixed-point experimental testing (FPET) is then conducted to indicate the correctness of simulation results. Subsequently, the DTSM-based vibration responses of the chute under different operating conditions are obtained. In this paper, the proposed strategy is employed to determine the occurrence of chain faults by amplitude comparisons, while failure patterns are distinguished by the adaptive optimal kernel time-frequency representation (AOKR).
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Tan, Wei, Ye Fen, and Qi Yuan. "Optimization of Historic Building Survey Technology under Artificial Intelligence Wireless Network Technology Environment." Wireless Communications and Mobile Computing 2021 (December 16, 2021): 1–12. http://dx.doi.org/10.1155/2021/6408772.
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In order to optimize the technology of the building, the damage identification of the building structure is studied. Firstly, back propagation neural network (BPNN) and information fusion technology are used to build neural network models. Secondly, the established model is trained. Finally, the displacement mode, natural frequency, Modal Assurance Criterion (MAC), and three kinds of information fusion with only one characteristic information are used as input data to analyse the results of BPNN identification damage. The results show that when the natural frequency is used as the sensitive feature of damage, the accuracy is the highest. The difference between the network output value and the expected value is the smallest, the network output is the most stable, and the network recognition effect is the best. The network output of a mixture of two damage depths is compared with the output of a single damage depth. The data of the network training set composed of the feature data with damage depth of 20 mm and 5 mm has higher accuracy and more accurate damage recognition. This research provides a reference for the optimization of building survey technology and has certain practical value.
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Yunus, M. A., M.N. Abdul Rani, M.A.S. Aziz Shah, M.S.M. Sani, and Z. Yahya. "The improvement of bolted joints model via finite element model updating method." Journal of Mechanical Engineering and Sciences 15, no. 4 (December 15, 2021): 8635–43. http://dx.doi.org/10.15282/jmes.15.4.2021.16.0682.
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Efficient schemes to represent mathematical model of thin-sheet metal structures jointed by bolted joints for accurately predict the structure dynamic behaviour has been a significant unresolved issue in structural dynamics community. The biggest challenge is to efficiently incorporate the joints local deformation effects on the developed mathematical model via finite element (FE) method. Generally, the joints local deformation typically exerts on the joints mating area. To solve this issue, this paper proposes efficient schemes to represent mathematical model of thin-sheet metal structures jointed by bolted joints with application to accurately calculate the structure dynamic behaviour using FE model updating method. The initial FE model of the assembled structure was developed by employed Fastener Connector (CFAST) in MSC NASTRAN software to represent the bolted joints while, the inclusion of the local deformation effects at the bolted joints mating area was represented by contact elements. Then, the responses obtained from the FE model was evaluated by weight up with experimental data. FE model updating (FEMU) method then was utilised for minimising prediction discrepancies originated from the initial FE model based on the experimental data. The proposed scheme shows the accuracy of the initial prediction was improved from 25.03 % to 14.65 % while the accuracy of the predicted mode shapes via modal assurance criterion (MAC) analysis were above 0.8. Therefore, the findings offer useful schemes for improving the quality of predicted dynamic behaviour, particularly in the thin-sheet metal jointed structure and the developed model can be used with confident for any subsequence dynamic analyses.
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PITCHAIAH, DASARIPALLE, and PUTTI SRINIVASA RAO. "OPTIMIZED DEEP LEARNING WITH OPPOSITION-BASED ANT LION APPROACH FOR CRACK IDENTIFICATION OF THICK BEAMS." Surface Review and Letters 27, no. 08 (January 22, 2020): 1950194. http://dx.doi.org/10.1142/s0218625x19501944.
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Crack identification in thick beams has improved increasing considerations from the scientific and building areas since the unpredicted structural failure may cause disastrous, catastrophic and life trouble. The goal of the present examination is to predict the unknown crack location and its depth in thick beams from the information of frequency data obtained from experimental examination. The effectiveness of the proposed strategy is approved by numerical simulations in view of experimental data for a cantilever beam, free-free beam and simply supported beam. With the improvements in delicate figuring, optimization strategies are acknowledged to be an extremely proficient instrument to offer an answer for crack identification issue. In the simulation modeling, the parameters, for example, shift; modal assurance criterion (MAC) and stiffness, are predicted by utilizing optimized deep learning neural network (ODNN) approach in view of crack location and size. To improve the weight in DLNN, the opposition-based ant lion (OAL) is used by minimizing the mean square error (MSE) rate. The result shows that the proposed model achieves the optimal performance compared with existing techniques.
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Denimal, E., L. Nechak, J. J. Sinou, and S. Nacivet. "Kriging Surrogate Models for Predicting the Complex Eigenvalues of Mechanical Systems Subjected to Friction-Induced Vibration." Shock and Vibration 2016 (2016): 1–22. http://dx.doi.org/10.1155/2016/3586230.
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This study focuses on the kriging based metamodeling for the prediction of parameter-dependent mode coupling instabilities. The high cost of the currently used parameter-dependent Complex Eigenvalue Analysis (CEA) has induced a growing need for alternative methods. Hence, this study investigates capabilities of kriging metamodels to be a suitable alternative. For this aim, kriging metamodels are proposed to predict the stability behavior of a four-degree-of-freedom mechanical system submitted to friction-induced vibrations. This system is considered under two configurations defining two stability behaviors with coalescence patterns of different complexities. Efficiency of kriging is then assessed on both configurations. In this framework, the proposed kriging surrogate approach includes a mode tracking method based on the Modal Assurance Criterion (MAC) in order to follow the physical modes of the mechanical system. Based on the numerical simulations, it is demonstrated by a comparison with the reference parameter-dependent CEA that the proposed kriging surrogate model can provide efficient and reliable predictions of mode coupling instabilities with different complex patterns.
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Gasparetto, Victor E. L., Marcela Machado, and Sergio H. S. Carneiro. "Experimental Modal Analysis of an Aircraft Wing Prototype for SAE Aerodesign Competition." DYNA 87, no. 214 (July 1, 2020): 100–110. http://dx.doi.org/10.15446/dyna.v87n214.85833.
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This work presents an experimental modal analysis of an aircraft wing prototype, designed by the Aerodesign team of the University of Brasilia, and performs a ground vibration testing of the prototype. The dynamic response data were acquired using the software LabVIEW, and the modal parameters were identified through the EasyMod toolbox. The modal parameters are characterised for the first seven vibration modes of the structure, with the firsts two being suspension modes of vibration. The effect of small changes in the experimental procedure on the identified modal parameters is discussed. It was observed that the use of an excitation signal as a logarithmic sine sweep and with a frequency range of excitation between 2 to 150 Hz resulted in less noise and more accurate measurement of the structure’s response. Results for different modal identification methods were verified using the Modal Assurance Criterion (MAC), and good correlation was achieved.
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Filippoupolitis, Marios, and Carl Hopkins. "Experimental Validation of Finite Element Models for Reinforced Concrete Beams with Discontinuities That Form Dowel-Type Joints." Vibration 4, no. 3 (July 5, 2021): 537–50. http://dx.doi.org/10.3390/vibration4030032.
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Earthquakes have the highest rate of mortality among the natural disasters and regularly lead to collapsed structures with people trapped inside them. When a reinforced concrete building collapses due to an earthquake, many of the concrete elements (i.e., beams and columns) are damaged and there are large sections where the concrete is missing and the steel reinforcement is exposed (i.e., concrete discontinuities). The prediction of vibration transmission in collapsed and severely damaged reinforced-concrete buildings could help decisions when trying to detect trapped survivors; hence there is need for experimentally validated finite element models of damaged concrete elements. This paper investigates the dynamic behaviour of damaged reinforced concrete beams using Experimental Modal Analysis (EMA) and Finite Element Methods (FEM). FEM models are assessed using two beams with one or more concrete discontinuities that form dowel-type joints. These models used either beam or spring elements for the exposed steel bars and were experimentally validated against EMA in terms of eigenfrequencies and mode shapes. Improved agreement was achieved when using springs instead of beam elements in the FEM model. The comparison of mode shapes used the Partial Modal Vector Ratio (PMVR) as a supplement to the Modal Assurance Criterion (MAC) to confirm that spring elements provide a more accurate representation of the response on all concrete parts of the beams.
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Chen, Yuan, and Xudong Mou. "Natural characteristics analysis and experimental test of spiral bevel gear pair in the tractor transmission system." Advances in Mechanical Engineering 13, no. 8 (August 2021): 168781402110371. http://dx.doi.org/10.1177/16878140211037120.
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Spiral bevel gear is widely used in various mechanical transmission systems, such as tractor transmission system. Because it is mainly used in the heavy-load conditions, it would most likely resonate within the rated speed, resulting in tooth fatigue damage. In this paper, based on the principle of meshing and gear tooth machining, the spherically involute tooth profile equation of spiral bevel gear is deduced and the precise modeling method based on the CATIA is studied. The natural frequency and modal shape under free vibration are obtained by the finite element method (FEM), the influence of web thickness and web hole on the natural frequency of driven gear plate is analyzed as well. In addition, the experimental modal of bevel gear pair is carried out based on a multiple-reference impact test, Modal Assurance Criterion (MAC) is calculated, the three-dimensional modeling accuracy and the finite element analysis reliability are verified. The results show that the error between the measured frequency of bevel gear pair and the calculated frequency of the finite element simulation are both within 5%, and the MAC is above 0.8. The fourth-order natural frequency is the most sensitive to the web thickness, the second-order natural frequency is the most sensitive to the web hole.
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Komarizadehasl, Seyedmilad, Pierre Huguenet, Fidel Lozano, Jose Antonio Lozano-Galant, and Jose Turmo. "Operational and Analytical Modal Analysis of a Bridge Using Low-Cost Wireless Arduino-Based Accelerometers." Sensors 22, no. 24 (December 14, 2022): 9808. http://dx.doi.org/10.3390/s22249808.
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Arduino-based accelerometers are receiving wide attention from researchers to make long-term Structural Health Monitoring (SHM) feasible for structures with a low SHM budget. The current low-cost solutions found in the literature share some of the following drawbacks: (1) high noise density, (2) lack of wireless synchronization, (3) lack of automatic data acquisition and data management, and (4) lack of dedicated field tests aiming to compare mode shapes from Operational Modal Analysis (OMA) with those of a digital model. To solve these problems, a recently built short-span footbridge in Barcelona is instrumented using four Low-cost Adaptable Reliable Accelerometers (LARA). In this study, the automatization of the data acquisition and management of these low-cost solutions is studied for the first time in the literature. In addition, a digital model of the bridge under study is generated in SAP2000 using the available drawings and reported characteristics of its materials. The OMA of the bridge is calculated using Frequency Domain Decomposition (FDD) and Covariance Stochastic Subspace Identification (SSI-cov) methods. Using the Modal Assurance Criterion (MAC), the mode shapes of OMA are compared with those of the digital model. Finally, the acquired eigenfrequencies of the bridge obtained with a high-precision commercial sensor (HI-INC) showed a good agreement with those obtained with LARA.
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Putranto, Alan. "IDENTIFIKASI PARAMETER MODAL DAN KERUSAKAN STRUKTUR OLEH BEBAN OPERASIONAL." Jurnal Teknik Sipil 15, no. 3 (October 4, 2020): 176–84. http://dx.doi.org/10.24002/jts.v15i3.3731.
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Perilaku dinamik dan identifikasi sistem merupakan isu yang sangat penting bagi para praktisi teknik sipil terutama enjinir struktur. Identifikasi sistem menggunakan metode Second order blind identification (SOBI) merupakan metode non parametrik domain waktu yang digunakan sebagai analisis modal operasional (OMA) pada penelitian struktur truss rangka bidang guna mengestimasi parameter modal struktur yang diberikan input beban sembarang dan tak terukur (ambient vibration).Metode SOBI divalidasi dengan finite element (FE) kemudian digunakan untuk memprediksi nilai parameter modal struktur model eksperimen.Hasil data rekaman respon struktur normal dan rusak menggunakan USB akselerometer X16-1D kemudian diolah dan data tersebut dilakukan load ke program matlab ExpNor15mts.m dan ExpDmg15mts.m sehingga dihasilkan parameter modal struktur. Parameter modal struktur tersebut pada saat keadaan struktur normal untuk nilai frekuensi dan ragam getar secara berturut-turut adalah 68,6925 rad/s dan 40,7983, sedangkan pada saat kondisi rusak diperoleh 50,9254 rad/s dan 30,9473. Nilai rasio frekuensi mengalami penurunan sebesar 34,8884 %. Pada penelitian ini, deteksi kerusakan hanya didasarkan pada rasio frekuensi. Deteksi kerusakan tidak dapat dilihat dari nilai modal assurance criterion (MAC) karena hanya memiliki satu nilai ragam getar.Metode SOBI cukup akurat untuk estimasi parameter modal struktur terutama frekuensi, tetapi hanya bisa mengestimasi nilai rasio redaman yang sangat kecil dan kurang efektif untuk estimasi ragam getar kedua dan ketiga.