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1
Zhou, Jun Wei, Lin He, and Rong Wu Xu. "Typical Errors Analysis in Frequency Response Function Measurement." Applied Mechanics and Materials 419 (October 2013): 470–76. http://dx.doi.org/10.4028/www.scientific.net/amm.419.470.
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FRF measurements can suffer from various errors. The effect of deterministic errors become more prominent compared to random errors in FRF measurement. Excitation and sensor misalignment is the most common source of deterministic error, so mathematic model is established and the effect on FRF estimation was analyzed for senor and excitation misalignment situations. Finite element model simulation reveals that misalignment error can have the least effect on the dominant FRFs and a stronger effect on lesser FRFs, beside that it also results in the appearance of false peaks in the measured FRFs.
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Zhang, Qingxia, Jilin Hou, Zhongdong Duan, Łukasz Jankowski, and Xiaoyang Hu. "Road Roughness Estimation Based on the Vehicle Frequency Response Function." Actuators 10, no. 5 (2021): 89. http://dx.doi.org/10.3390/act10050089.
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Road roughness is an important factor in road network maintenance and ride quality. This paper proposes a road-roughness estimation method using the frequency response function (FRF) of a vehicle. First, based on the motion equation of the vehicle and the time shift property of the Fourier transform, the vehicle FRF with respect to the displacements of vehicle–road contact points, which describes the relationship between the measured response and road roughness, is deduced and simplified. The key to road roughness estimation is the vehicle FRF, which can be estimated directly using the measured response and the designed shape of the road based on the least-squares method. To eliminate the singular data in the estimated FRF, the shape function method was employed to improve the local curve of the FRF. Moreover, the road roughness can be estimated online by combining the estimated roughness in the overlapping time periods. Finally, a half-car model was used to numerically validate the proposed methods of road roughness estimation. Driving tests of a vehicle passing over a known-sized hump were designed to estimate the vehicle FRF, and the simulated vehicle accelerations were taken as the measured responses considering a 5% Gaussian white noise. Based on the directly estimated vehicle FRF and updated FRF, the road roughness estimation, which considers the influence of the sensors and quantity of measured data at different vehicle speeds, is discussed and compared. The results show that road roughness can be estimated using the proposed method with acceptable accuracy and robustness.
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Juraj, Úradníček, Miloš Musil, and Michal Bachratý. "Frequency Response Function Measurement on Simplified Disc Brake Model." Strojnícky casopis – Journal of Mechanical Engineering 68, no. 3 (2018): 225–30. http://dx.doi.org/10.2478/scjme-2018-0036.
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AbstractThe paper describes role of non-proportional damping in flutter type instability, demonstrated on simplified disc brake model. The discrete two degrees of freedom system is considered to imply damping induced instability through a system eigenvalues evaluation. The Frequency Response Function (FRF) is further calculated from measurements on the physical disc brake model. From FRF, damping properties are estimated and discussed. Several different loading states of the pad versus disc are considered to show loading impact on FRF and thus damping of the system.
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Wan Iskandar Mirza, W. I. I., M. N. Abdul Rani, M. A. Yunus, R. Omar, and M. S. Mohd Zin. "Alternative scheme for frequency response function measurement of experimental-analytical dynamic substructuring." Journal of Mechanical Engineering and Sciences 13, no. 2 (2019): 4946–57. http://dx.doi.org/10.15282/jmes.13.2.2019.13.0410.
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The accuracy of the predicted dynamic behaviour of an assembled structure using the frequency based substructuring (FBS) method is often found to be diverged from the experimental counterparts. The divergence which has become the paramount concern and major issue for structural dynamicists is because of the unreliable experimental FRF data of the interfaces of substructures, arising from the limited resources of appropriate excitation points and accelerometer attachments in the vicinity of the interfaces. This paper presents an alternative scheme for FRF measurement of the experimental FRF data of substructures. In this study, an assembled structure consisting of two substructures were used, namely substructure A (Finite element model) and substructure B (Experimental model). The FE model of substructure A was constructed by using 3D elements and the FRFs were derived via the FRF synthesis method. Specially customised bolts were used to allow the attachment of accelerometers and excitation to be made at the interfaces of substructure B, and the FRFs were measured by using impact testing. Both substructures A and B were then coupled by using the FBS method and the coupled FRF was validated with the measured FRF counterparts. This work revealed that the proposed scheme with specially customized bolts has led to a significant enhancement and improvement in the FBS predicted results.
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Steffensen, M. T., D. Tcherniak, and J. J. Thomsen. "Accurate frequency response function estimation using noise measurements in experimental modal analysis." Journal of Physics: Conference Series 2647, no. 21 (2024): 212003. http://dx.doi.org/10.1088/1742-6596/2647/21/212003.
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Abstract In experimental structural dynamics, reliable estimation of Frequency Response Functions (FRF) is important to correctly characterize a mechanical system. In Experimental Modal Analysis (EMA), the FRFs are used as input to a modal parameter estimation algorithm to obtain the modal characteristics of the system. Errors due to noisy measurements are inevitably present in the FRFs and propagate to the modal parameters. A consistent FRF-estimator with low uncertainty is therefore needed. Different FRF estimators have been proposed with some consistency when certain noise-related assumptions are fulfilled (H1, H2, etc.). To choose the appropriate frequency response function estimator, information about the noise in the experimental setup is desirable. In this work it is shown how to use measurements of noise, to characterize different noise components in the experimental setup and determine the appropriate number of averages needed for the experimental setup. The identified noise components can be used to identify the main source of uncertainty in the experimental setup and which FRF estimator to use.
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Zhang, Yan, Jijian Lian, Songhui Li, Yanbing Zhao, Guoxin Zhang, and Yi Liu. "Predicting Dam Flood Discharge Induced Ground Vibration with Modified Frequency Response Function." Water 13, no. 2 (2021): 144. http://dx.doi.org/10.3390/w13020144.
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Ground vibrations induced by large flood discharge from a dam can damage surrounding buildings and impact the quality of life of local residents. If ground vibrations could be predicted during flood discharge, the ground vibration intensity could be mitigated by controlling or tuning the discharge conditions by, for example, changing the flow rate, changing the opening method of the orifice, and changing the upstream or downstream water level, thereby effectively preventing damage. This study proposes a prediction method with a modified frequency response function (FRF) and applies it to the in situ measured data of Xiangjiaba Dam. A multiple averaged power spectrum FRF (MP-FRF) is derived by analyzing four major factors when the FRF is used: noise, system nonlinearity, spectral leakages, and signal latency. The effects of the two types of vibration source as input are quantified. The impact of noise on the predicted amplitude is corrected based on the characteristics of the measured signal. The proposed method involves four steps: signal denoising, MP-FRF estimation, vibration prediction, and noise correction. The results show that when the vibration source and ground vibrations are broadband signals and two or more bands with relative high energies, the frequency distribution of ground vibration can be predicted with MP-FRF by filtering both the input and output. The amplitude prediction loss caused by filtering can be corrected by adding a constructed white noise signal to the prediction result. Compared with using the signal at multiple vibration sources after superimposed as input, using the main source as input improves the accuracy of the predicted frequency distribution. The proposed method can predict the dominant frequency and the frequency bands with relative high energies of the ground vibration downstream of Xiangjiaba Dam. The predicted amplitude error is 9.26%.
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Zhang, Yan, Jijian Lian, Songhui Li, Yanbing Zhao, Guoxin Zhang, and Yi Liu. "Predicting Dam Flood Discharge Induced Ground Vibration with Modified Frequency Response Function." Water 13, no. 2 (2021): 144. http://dx.doi.org/10.3390/w13020144.
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Ground vibrations induced by large flood discharge from a dam can damage surrounding buildings and impact the quality of life of local residents. If ground vibrations could be predicted during flood discharge, the ground vibration intensity could be mitigated by controlling or tuning the discharge conditions by, for example, changing the flow rate, changing the opening method of the orifice, and changing the upstream or downstream water level, thereby effectively preventing damage. This study proposes a prediction method with a modified frequency response function (FRF) and applies it to the in situ measured data of Xiangjiaba Dam. A multiple averaged power spectrum FRF (MP-FRF) is derived by analyzing four major factors when the FRF is used: noise, system nonlinearity, spectral leakages, and signal latency. The effects of the two types of vibration source as input are quantified. The impact of noise on the predicted amplitude is corrected based on the characteristics of the measured signal. The proposed method involves four steps: signal denoising, MP-FRF estimation, vibration prediction, and noise correction. The results show that when the vibration source and ground vibrations are broadband signals and two or more bands with relative high energies, the frequency distribution of ground vibration can be predicted with MP-FRF by filtering both the input and output. The amplitude prediction loss caused by filtering can be corrected by adding a constructed white noise signal to the prediction result. Compared with using the signal at multiple vibration sources after superimposed as input, using the main source as input improves the accuracy of the predicted frequency distribution. The proposed method can predict the dominant frequency and the frequency bands with relative high energies of the ground vibration downstream of Xiangjiaba Dam. The predicted amplitude error is 9.26%.
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Ślaski, Grzegorz, and Zbyszko Klockiewicz. "The influence of shock absorber characteristics’ nonlinearities on suspension Frequency Response Function estimation and possibilities of simplified characteristics modelling." Archives of Automotive Engineering – Archiwum Motoryzacji 96, no. 2 (2022): 77–95. http://dx.doi.org/10.14669/am/151704.
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The paper shortly presents shock absorber design evolution and resulting achieved characteristics. The way in which suspension performance is evaluated is described giving information about models used for suspension parameter tuning during simulation testing of suspension transmissibility (FRF - Frequency Response Function) for most important suspension assessment criteria. More detailed information about models of shock absorber (damper) nonlinearities of characteristics allows for description of methods of linear and nonlinear suspension models FRF estimation. Testing linear suspension model is possible with the use of analytical transfer function formulas which were used to verify methods for estimation FRF using estimated power spectral density functions of excitation and response signals. Designing appropriate input signal allowing to get useful response signals was necessary to for the success of this research. Proposed FRF estimation method was used for linear estimation of nonlinear suspension for a given range of working condition. It was demonstrated that there is no single value of a damping coefficient which would make the linear model responses similar to the responses of the nonlinear one. Then the bilinear model was proposed, giving good damper static nonlinear characteristic.
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Li, Xin Hui, Tie Jun Yang, Jian Chao Dong, and Ze Qi Lu. "Secondary Path Estimation by PCA-Compressed Frequency Response Function in Active Vibration Control." Applied Mechanics and Materials 66-68 (July 2011): 721–26. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.721.
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The FXLMS algorithm is widely used in active vibration control system. The estimation of secondary path plays very important roles in such a system. This paper presents an experimental investigation of effective secondary path estimation in active vibration control using measured Frequency Response Function (FRF). Principal component analysis (PCA) is pursued to the measured FRF for noise elimination, and then the PCA-compressed FRF data are used for secondary path estimation. The control results indicate that the proposed method has good control performance.
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Jia, Libin, Jeffrey D. Naber, and Jason R. Blough. "Frequency response function adaptation for reconstruction of combustion signature in a 9-L diesel engine." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 17 (2015): 3071–83. http://dx.doi.org/10.1177/0954406215569256.
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An accelerometer as a low-cost non-intrusive transducer for sensing the combustion events in a diesel engine was investigated via the reconstruction of in-cylinder pressure using an adapting frequency response function (FRF). As the noise introduced into the accelerometer signal and the response to combustion vary with the operating condition, the FRF computed from a single operating condition only works for the same or similar conditions. To overcome this limitation, an adaptation process for the FRF was explored. Robustness of FRF over additional operational conditions with start of injection, start of combustion, and load variations was greatly improved. Frequency domain analysis shows that only the low-frequency content is determinant for the in-cylinder pressure reconstruction, and the adaptation of the first and second (0 Hz and 121 Hz) harmonics of the FRF results in the greatest improvement for the in-cylinder pressure estimation accuracy. The 0 Hz harmonic is adjusted based on the pre-measured in-cylinder pressure offset and the online measured accelerometer signal offset. Particle swam optimization as a computational algorithm is applied to adapt the 121 Hz harmonic of FRF. The results show that the adapted FRF, in comparison to the unadapted FRF, can reduce the phase error up to 1.3 crank angle degrees and reduce the amplitude error by up to 90%.
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Chen, Jian Qiu, and Ping Tan. "Identification of Frequency Response Function of Shaking Table with a New Estimator." Applied Mechanics and Materials 44-47 (December 2010): 719–23. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.719.
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Shaking table is a nonlinear system, which is a more nonlinear system with payload. System can be usually as linear system nearby working point in control strategy. 1 H -estimator or 2 H -estimator is used for identifying the Frequency Response Function (FRF) of the system. 1 H -estimator is a lower-estimator and 2 H -estimator is an over-estimator, both have large estimating errors. In this paper, a new estimator, m H -estimator, is used for the identification of the shaking table system’s FRF, and whose parameters are estimated by differential evolution (DE) which makes m H closed to the true FRF H . This control strategy can reduce the steps of iterative learning control (ILC) of shaking table system, and the affection of payload characteristic.
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Xuan, Xiao-Jian, Zhe-Hao Haung, Kung-Da Wu, and Jui-Pin Hung. "Prediction of the Frequency Response Function of a Tool Holder-Tool Assembly Based on Receptance Coupling Method." Engineering, Technology & Applied Science Research 8, no. 6 (2018): 3556–60. https://doi.org/10.5281/zenodo.2532646.
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Regenerative chatter has a fatal influence on machine performance in high-speed milling process. Basically, machining condition without chattering can be selected from the stability lobes diagram, which is estimated from the tool point frequency response function (FRF). However, measurements of the tool point FRF would be a complicated and time-consuming task with less efficiency. Therefore prediction of the tool point FRF is of importance for further calculation of the machining stability. This study employed the receptance coupling analysis method to predict the FRF of a tool holder-tool module, which is normally composed of substructures, tool holder and cutter with different length. In this study, the angular components of FRFs of the substructures required for coupling operation were predicted by finite element analysis, apart from the translational components measured by vibration experiments. Using this method, the effects of the overhang length of the cutter on the dynamic characteristics have been proven and successfully verified by the experimental measurements. The proposed method can be an effective way to accurately predict the dynamic behavior of the spindle tool system with different tool holder-tool modules.
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Zhao, Yu, and Zhenrui Peng. "Frequency Response Function-Based Finite Element Model Updating Using Extreme Learning Machine Model." Shock and Vibration 2020 (October 5, 2020): 1–10. http://dx.doi.org/10.1155/2020/8526933.
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A frequency response function- (FRF-) based surrogate model for finite element model updating (FEMU) is presented in this paper. Extreme learning machine (ELM) is introduced as the surrogate model of the finite element model (FEM) to construct the relationship between updating parameters and structural responses. To further improve the generalization ability, the input weights and biases of ELM are optimized by Lévy flight trajectory-based whale optimization algorithm (LWOA). Then, LWOA is also applied to obtain the best updating results, where the objective function is defined by the difference between analytical FRF data and experimental data. Finally, a plane truss is used to demonstrate the performance of the proposed method. The results show that, compared with second-order response surface (RS), radial basis function (RBF), traditional ELM, and other optimized ELM, a LWOA-ELM model has higher prediction accuracy. After updating, the FRF data and frequencies have a significant match to the experimental model. The proposed FEMU method is feasible.
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Jia, Hai Lei, and Yin Zhao. "Detection of Damage Extension in Cantilever Beams Using Change Ratio of Frequency Response Functions." Applied Mechanics and Materials 50-51 (February 2011): 875–79. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.875.
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Frequency response function (FRF) is a fundamental dynamic index, which is capable of reflecting structural dynamic properties using full-spectrum information. In spite of distinct merits over conventional modal parameters, the FRF has an observable drawback of multi-dimensionality, unsuited for damage characterization. Such a situation motivates an interesting subject, i.e., extracting low-dimensional, high-sensitivity damage index from the FRF. This study focuses on developing a valid damage index, called FRF change ratio, to detect extension of damage. An experiment towards cantilever beams is systemically conducted. The results show that the FRF change ratio can effectively reflects damage extension, and it is more sensitive than conventional natural frequencies. This new damage index holds promise for practical damage detection in beam-like structures.
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Wu, Kuangcheng. "Advanced numerical techniques for predicting frequency response functions." Journal of the Acoustical Society of America 154, no. 4_supplement (2023): A179. http://dx.doi.org/10.1121/10.0023189.
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Numerical methods have been widely used to predict Frequency Response Functions (FRF) of structures. The FRF can be used to characterize structural dynamics and support sound and vibration control. Generally, frequency sweep is conducted in the FRF calculations to identify damping and resonant frequencies of structures under excitations. However, as numerical models are getting complex and larger, the demands for computational resources (e.g., CPU time, memory, disk space) are greatly increased. Lately, high performance computing (HPC) at the DoD HPC center has been used with advanced numerical techniques to reduce the overall computational time. Those advanced numerical techniques include Krylov subspace and Galerkin Projection (KGP) and Pade Approximation. Significantly CPU time reduction has been demonstrated for relatively smaller FE models. This paper will further discuss adaptive KGP by automating the frequency sweep process via calculated relative residues, then combine with Finite Element Tearing and Interconnecting (FETI) to solve for FRF of a large FEM model in the order of 60M DOF. A flat plate with viscoelastic layer will serve as an example to demonstrate accuracy and efficiency of AKGP with FETI. The benefits of using HPC with advanced numerical techniques to solve for large FEM models are clearly displayed.
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Wang, Xiong, Wei Liu, Jifeng Ding, Yi Sun, and Yongbing Dang. "Pyroshock Response Prediction of Spacecraft Structure in Wide Frequency Domain Based on Acceleration FRF." Aerospace 9, no. 2 (2022): 54. http://dx.doi.org/10.3390/aerospace9020054.
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The initiating explosive shock environment of an aerospace mission has the characteristics of instantaneity, high amplitude and a wide frequency domain. An improved method based on the acceleration frequency response function (FRF) and virtual mode synthesis method (VMSS) is proposed to predict the pyroshock response of a spacecraft structure in a wide frequency domain. Firstly, the statistical energy analysis (SEA) model of the spacecraft structure was established, and the FRF and modal density of the model were obtained. Then, the paper explains how, due to the small number of modes in the low-frequency band, the calculation results of the SEA method in the low-frequency band were not accurate enough. The FRF of the SEA model in the low-frequency band was modified by an FRF test of the structure. Finally, the shock response spectrum (SRS) was obtained based on the VMSS and the modified FRF. A shock experiment on the spacecraft structure was conducted by using the shock experiment system, which is based on a light-gas gun. The accurate shock force function and acceleration response results were obtained. The numerical results based on the improved method are in line with those in the experiment. This verifies that the novel method can better grasp the response characteristics of the structure in the broadband domain. The novel method effectively improves the response prediction accuracy of the SEA model in the relatively low-frequency band. While ensuring the computational efficiency, more accurate shock response results in a wide frequency domain were obtained. The novel method presented in this paper provides support of numerical analysis for pyroshock response prediction of spacecraft structure in a wide frequency domain.
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Khiem, Nguyen Tien, Tran Thanh Hai, Nguyen Thi Lan, Ho Quang Quyet, Ha Thanh Ngoc, and Pham Van Kha. "Frequency response function of cracked Timoshenko beam measured by a distributed piezoelectric sensor." Vietnam Journal of Mechanics 46, no. 1 (2024): 15–30. http://dx.doi.org/10.15625/0866-7136/20575.
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In the present report, a novel concept of frequency response function (FRF) is introduced for piezoelectric beam. First, a model of Timoshenko beam bonded with a piezoelectric layer is established and used for deriving the conventional frequency response function acknowledged as mechanical frequency response function (MERF). Then, the output charge produced in the piezoelectric layer is calculated from the MFRF and therefore obtained frequency-dependent function is called electrical frequency response function (EFRF) for the integrated beam. This concept of FRF depends only on exciting position and can be explicitly expressed through crack parameters. So that it provides a novel instrument to modal analysis and structural health monitoring of electro-mechanical systems, especially for crack detection in beams using distributed piezoelectric sensor. The sensitivity of EFRF to crack has been examined and illustrated in numerical examples for cracked Timoshenko beam.
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Kao, Ching-Yun, Xuan-Zhi Chen, and Shih-Lin Hung. "A Displacement Frequency Response Function-Based Approach for Locating Damage to Building Structures." Advances in Civil Engineering 2020 (March 17, 2020): 1–23. http://dx.doi.org/10.1155/2020/4509576.
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Frequency response function (FRF) data can provide considerably more information on damage in the desired frequency range as compared to modal data extracted from a very limited range around resonances. Among structural health monitoring techniques, FRF-based methods have the potential to locate structural damage. Conventional structural damage detection technology collects structural response data using contact systems, such as displacement or acceleration transducers. However, installing these contact systems can be costly in terms of labor, cost, and time. Several noncontact measurement technologies, such as optical, laser, radar, and GPS, have been developed to overcome these obstacles. Given the rapid advances in optical imaging hardware technology, the use of digital photography in structural monitoring systems has attracted considerable attention. This study develops a displacement FRF-based approach to locate damage to building structures. The proposed damage location index, CurveFRFDI, improves the sensitivity of SubFRFDI, which is a substructure FRF-based damage location index proposed by Lin et al. (2012). Moreover, the feasibility of applying the proposed approach to locate damage to building structures using displacement measured by a digital camera combined with digital image correlation techniques is also investigated in this study. A numerical example and an experimental example are presented to demonstrate the feasibility of using the proposed approach to locate damage to building structures for single and multiple nonadjacent damage locations.
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Zou, Wan Jie, Zhen Luo, and Guo En Zhou. "Study on Benchmark Structure Damage Identification Base on Frequency Response Function and Genetic Algorithm." Advanced Materials Research 163-167 (December 2010): 2765–69. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.2765.
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A combined method for the Benchmark structure damage identification base on the frequency response function(FRF) and genetic algorithm(GA) is presented. The reducing factors of element stiffness are used as the optimization variables, and the cross signature assurance criterion (CSAC) of the test FRF and the analysis FRF is used to constructing the optimization object function and the fitness function of the GA. To avoid the weakness of binary encoding, the floating point number encoding is used in the GA. At last, the Benchmark structure established by IASC-ASCE SHM group is caculated by the proposed method, the results show that even if the serious testing noise is considered, the patterns of damage of the Benchmark structure can be identified well. The effectiveness of the presented method is verified.
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Zhang, Erliang, Jiayu Zhang, Cheng Ren, and Hsinshen Ho. "A Spatial-Frequency Approach to Point-Wise Frequency Response Function Estimation with Digital Image Correlation." Applied Sciences 14, no. 20 (2024): 9212. http://dx.doi.org/10.3390/app14209212.
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The use of digital image correlation for modal analysis is becoming an appealing option thanks to its non-contact and full-field measurement process. However, frequency response function (FRF) estimation can be challenging due to the limited number of time domain data and heavy measurement noise. Thereby, the present work aims to propose a method which improves the estimation accuracy of point-wise FRFs. Firstly, a Gaussian-process-based spatial-frequency model is proposed, which makes use of the intrinsic properties of the FRF and the local spatial information of field measurements. Then, a Bayesian solution is developed, which is enforced by a stable and efficient numerical procedure. Finally, the effectiveness of the proposed method is verified by making a comparison with the spectral estimator through the use of simulated data, and it is further validated based on an experimental application.
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Asma, Farid, and Amar Bouazzouni. "Finite Element Model Updating Using FRF Measurements." Shock and Vibration 12, no. 5 (2005): 377–88. http://dx.doi.org/10.1155/2005/581634.
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This study presents a new updating method based on measured frequency response functions. The objective function of the minimization procedure is formed by the difference between the measured and the analytical frequency responses. The updating parameters are the correction coefficients related to each the elementary mass and stiffness matrices. While making use of a number of incomplete measurements for some frequencies, one builds a non-linear system of equations. The linearisation of the numerical system leads to an iterative procedure. An intrinsic frequency parametrization is proposed in order to accelerate the convergence of the iterative system. The obtained results are comparable with those of the known least squares methods.
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Hou, Yihong, Chunxue Wang, Peng Duan, et al. "A General Method to Obtain the Frequency Response Function from the Disturbance Source to the Sensitive Payload." Applied Sciences 13, no. 8 (2023): 4844. http://dx.doi.org/10.3390/app13084844.
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Microvibrations are one of the main factors contributing to platform jitter and a decline in pointing stability and precision. Among various disturbance sources, reaction wheel assembly (RWA) is one of the most significant ones and has drawn the interest of numerous scholars. How to evaluate the influence of the disturbances of RWA on the pointing accuracy of a spacecraft is an arduous task because it involves multiple disciplines. The acquisition of the frequency response function (FRF) from the disturbance source to the sensitive payload is one of the most crucial stages in integrated modeling. Direct measurement of the FRF in the six directions is challenging because of the restricted room for RWA installation in a spacecraft, particularly in small satellites. In this paper, a general method based on the Hv algorithm to obtain the FRF is presented. This method only needs the RWA, itself, as an excitation source. Then, in order to acquire the FRF, we use an optical remote-sensing satellite as the research object. The peak positions of FRF obtained by different RWAs are basically the same, while the amplitudes are slightly different, indicating that this method is effective. This method takes into consideration the coupling between the RWA and the spacecraft, making it possible to multiply the RWA disturbance measured at a fixed interface with the FRF, to determine the image motion of the sensitive payload.
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Huizinga, A. T. M. J. M., D. H. van Campen, and A. de Kraker. "Application of Hybrid Frequency Domain Substructuring for Modelling an Automotive Engine Suspension." Journal of Vibration and Acoustics 119, no. 3 (1997): 304–10. http://dx.doi.org/10.1115/1.2889724.
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A practical application of hybrid FRF-coupling (Frequency Response Function) in the development of a passenger car is presented. First, a short review is given about FRF-coupling in general. Next, some problems are discussed which may be encountered when both analytical and experimental FRF-data is used in FRF-coupling. This is also known as hybrid modelling. The main part of this paper presents a successful application of hybrid FRF-coupling to analyze and solve an interior noise problem of a passenger car. Both analytical and experimental FRFs were used to create a hybrid dynamic model of a complete passenger car. The engine and its suspension system were modelled using finite elements, while the remainder of the car was modelled by experimentaly derived FRFs. This hybrid model was then used to compute the response of the vehicle due to the engine excitation. Measured noise transfer function were used next to compute the interior sound pressure level using forced response results of the hybrid car model. Subsequently, the hybrid model was used to analyze the problem, and to predict the effects of an alternative design of the engine suspension on interior noise. Numerical results indicated that the alternative design would have a significant positive effect on noise. This was confirmed by verification measurements on a car.
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Sulaiman, M. S. A., M. A. Yunus, A. R. Bahari, and M. N. Abdul Rani. "Identification of damage based on frequency response function (FRF) data." MATEC Web of Conferences 90 (December 20, 2016): 01025. http://dx.doi.org/10.1051/matecconf/20179001025.
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Horiguchi, Ryuzo, Yoshiro Oda, Keito Sato, Hiroto Kozuka, and Takao Yamaguchi. "Center Impedance Method for Estimating Complex Modulus with Wide Frequency Range and Large Loss Factors." Shock and Vibration 2021 (September 27, 2021): 1–23. http://dx.doi.org/10.1155/2021/1644823.
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A simple method for determining viscoelasticity over a wide frequency range using the frequency response function (FRF) mobility obtained by the center impedance method is presented. As user data comprise the FRF between the velocity of the excitation rod and excitation force, it is challenging to separate the signal and noise. Our proposed method is based on the FRF obtained from the analytical solution of the equation of motion of the viscoelastic beam and relationship between the complex wavenumber (real wavenumber and attenuation constant) of flexural wave and viscoelasticity. Furthermore, a large loss factor can be handled over a wide frequency range without using the half-power bandwidth. In this study, actual FRF mobility data containing noise were processed using preprocessing, inverse calculation, and postprocessing. Preprocessing removed low-coherence data, compensates for the effects of instrument gain, and transformed the FRF into its dimensionless equivalent. Then, inverse calculations were used to solve the mobility equation and determine the complex wavenumber. In postprocessing, the complex wavenumber obtained by the inverse calculation was curve fitted using functions with mechanical significance. Consequently, the storage modulus based on the curve-fitted complex wavenumber was a monotonically increasing frequency function. The loss factor had a smooth frequency dependence such that it has the maximum value at a single frequency. The proposed method can be applied to composite materials, where the application of time-temperature superposition is challenging. We utilized the measured FRF mobility data obtained over a duration of several seconds, and this method can also be applied to materials with large loss factors of 1 or more.
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Chen, Yu, Qiang Li Luan, Zhang Wei Chen, and Hui Nong He. "Power Spectra Density Replication Control Strategy for 2-Axis Hydraulic Shaker Based on HV Estimator." Applied Mechanics and Materials 596 (July 2014): 610–15. http://dx.doi.org/10.4028/www.scientific.net/amm.596.610.
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Hydraulic shaker, equipment of simulating laboratory vibration environment, can accurately replicate the given power spectral density (PSD) and time history with an appropriate control algorithm. By studying method Hv estimator of frequency response function (FRF) estimation, a FRF identification strategy based on the Hv estimator is designed to increase the convergence rapidity and improve the system response function specialty. The system amplitude-frequency characteristics in some frequency points or frequency bands have large fluctuation. To solve this issue, a step-varying and frequency-sectioning iterative correction control algorithm is proposed for the control of 2-axial exciter PSD replication tests and the results show that the algorithm has a good effect on the control of hydraulic shaker, and can achieve reliable and high-precision PSD replication.
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Melcer, Jozef, and Veronika Valašková. "Vehicle model response in frequency domain." MATEC Web of Conferences 313 (2020): 00009. http://dx.doi.org/10.1051/matecconf/202031300009.
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The offered article deals with one of the possibilities of numerical analysis of the vehicle response in frequency domain. It works with quarter model of vehicle. For the selected computational model of vehicle it quantifies the Frequency Response Functions (FRF) of both force and kinematic quantities. It considers the stochastic road profile. The Power Spectral Density (PSD) of the road profile is used as input value for the calculation of Power Spectral Density of the response. Al calculations are carried out numerically in the environment of program system MATLAB. When we know the modules of FRF or the Power Response Factors (PRF) of vehicle model the calculation of vehicle response in frequency domain is fast and efficient.
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Castro, L., P. Viéville, and Paul Lipiński. "Experimental Methodology Destined to Establish the Frequency Response Function (FRF) between a Dynamic Force and the Signals Emitted by a Piezoelectric Dynamometer." Materials Science Forum 526 (October 2006): 85–90. http://dx.doi.org/10.4028/www.scientific.net/msf.526.85.
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This paper proposes an experimental method for obtaining the Frequency Response Function (FRF) between a dynamic force and the signals emitted by a piezoelectric dynamometer. This function is known as Transmissibility. In the FRF obtaining stage, different configurations of mounting and excitation have been compared to improve the function quality. The method has been developed with a three components dynamometer fixed on a milling machine. The FRF has two principal applications: it is used to evaluate the measurement system accuracy and to correct the measurements, if necessary. The method has been developed with the purpose of studying the cutting forces in machining process. Furthermore, it has been identified the influence of the parts of the measurement chain in the measuring system response.
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Xuan, X. J., Z. H. Haung, K. D. Wu, and J. P. Hung. "Prediction of the Frequency Response Function of a Tool Holder-Tool Assembly Based on Receptance Coupling Method." Engineering, Technology & Applied Science Research 8, no. 6 (2018): 3556–60. http://dx.doi.org/10.48084/etasr.2372.
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Regenerative chatter has a fatal influence on machine performance in high-speed milling process. Basically, machine condition without chattering can be selected from the stability lobes diagram, which is estimated from the tool point frequency response function (FRF). However, measurements of the tool point FRF would be a complicated and time-consuming task with less efficiency. Therefore prediction of the tool point FRF is of importance for further calculation of the machining stability. This study employed the receptance coupling analysis method to predict the FRF of a tool holder-tool module, which is normally composed of substructures, tool holder and cutter with different length. In this study, the angular components of FRFs of the substructures required for coupling operation were predicted by finite element analysis, apart from the translational components measured by vibration experiments. Using this method, the effects of the overhang length of the cutter on the dynamic characteristics have been proven and successfully verified by the experimental measurements. The proposed method can be an effective way to accurately predict the dynamic behavior of the spindle tool system with different tool holder-tool modules.
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NAM, Jeongmin, Sangyoung PARK, and Yeonjune KANG. "Enhancing accuracy and robustness in FBS decoupling through Tikhonov regularization and unit balancing." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 270, no. 9 (2024): 2848–55. http://dx.doi.org/10.3397/in_2024_3240.
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Frequency-based Substructuring (FBS) enables the prediction of transfer functions for an assembled system based on those of a single-unit system. Conversely, FBS decoupling derives the frequency response function (FRF) of a single-unit system from the assembled system. This approach is valuable when obtaining the transfer functions of a system is challenging due to boundary conditions and deformation conditions. FBS decoupling can enhance accuracy by using additional indicator sensors. However, this often results in significant noise due to the ill-posed FRF matrix inversion. In this paper, Tikhonov regularization is employed to reduce noise-induced errors. Furthermore, this paper addresses the issue of inadequate Tikhonov regularization caused by the inherent scaling differences between the rotational and translational components within the FRF matrix. To rectify this challenge, a unit balancing method is proposed to mitigate the influence of scaling differences. This method enhances the accuracy and reliability of FRF matrix inversion processes, contributing to enhanced noise reduction and robustness in practical applications.
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Wang, Xin, Nan Wu, and Quan Wang. "Frequency Comparison Function Method for Real-Time Identification of Breathing Crack at Welding Joint." International Journal of Structural Stability and Dynamics 20, no. 13 (2020): 2041001. http://dx.doi.org/10.1142/s0219455420410011.
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In this research, the frequency comparison function (FCF) method is proposed and studied to realize high-sensitive real-time crack identification at the welding joint area for a beam-type structure. This method is derived from the frequency response function (FRF). During FCF, we use the response signal collected from the designated point of the structure instead of the excitation. The standard deviation of the FCF amplitude curve is calculated to detect and evaluate the possible crack and its induced vibration perturbations afterward. Vibration responses are simulated in ANSYS by the use of the finite element analysis of a welded beam structure, and these signals are then analyzed with the FCF algorithm. It is concluded that FCF is an efficient method for breathing crack identification and can be easily applied under different excitation conditions, including harmonic and random ones. Meanwhile, FCF can be applied without any pre-processing algorithms such as filtering and smoothing. So, it can be used for real-time crack identification. By combining the FCF with the smart coating sensor composed of piezoelectric layers, the crack identification with high sensitivity is realized. The crack is detectable at its very early stage (starting from 3% of the beam thickness). Experimental studies under harmonic and random excitations are processed, and the results prove high sensitivity and feasibility of the proposed crack detection method.
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Youn, Deokki, Usik Lee, and Oh Yang Kwon. "Experimental Verification of the Structural Damage Identification Method Developed for Beam Structures." Key Engineering Materials 326-328 (December 2006): 1113–16. http://dx.doi.org/10.4028/www.scientific.net/kem.326-328.1113.
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In this paper, an experimental verification has been conducted for a frequency response function (FRF)-based structural damage identification method (SDIM) proposed in the previous study [1]. The FRF-based SDIM requires the natural frequencies and mode shapes measured in the intact state and the FRF-data measured in the damaged state. Experiments are conducted for the cantilevered beam specimens with one and three slots. It is shown that the proposed FRF-based SDIM provides damage identification results that agree quite well with true damage state.
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Abidin, Zainal, Agusmian Partogi, and Noval Lilansa. "Validation of the FRF Magnetude Error in Vibration Impact Testing Using Numerical Simulation." Applied Mechanics and Materials 83 (July 2011): 224–29. http://dx.doi.org/10.4028/www.scientific.net/amm.83.224.
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Digital frequency analyzers are commonly used in FRF (Frequency Response Function) measurement using impact force method. The analyzers are inevitably generating errors due to limited spectral line as well as frequency span. The FRF magnitude error has been derived by Partogi [1] theoretically. This paper describes numerical simulation used to validate the theoretical equation. For this purpose, three numerical case studies have been simulated. Based on the results of simulation, the FRF magnitude errors can then be calculated and compared to those obtained from theoretical equation. The results show a perfect match between them so that, it can be concluded that the equation has been derived properly.
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Yu, M. C., X. Gao, and Q. Chen. "Nonlinear Frequency Response Analysis and Jump Avoidance Design of Molecular Spring Isolator." Journal of Mechanics 32, no. 5 (2016): 527–38. http://dx.doi.org/10.1017/jmech.2016.52.
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AbstractMolecular spring vibration isolation technology has been invented in the recent years but it still needs further development in dynamics theory. A molecular spring isolation (MSI) consists of water and hydrophobic zeolites as working medium, providing high-static-low-dynamic stiffness. The dynamic properties of MSI are thoroughly investigated in this paper. Firstly, the nonlinear dynamic model of a vibration system support by MSI, i.e. the equation of motion, is established. Then the averaging method is employed to estimate the frequency response function (FRF) of the primary resonance. The phase trajectories diagram evolvement of primary resonance is also investigated to analysis the stability of the primary resonance response. From the plot of FRF, it is found that there exists a jump phenomenon induced by nonlinear stiffness, which may have harmful impacts on the equipment which is supposed to be protected from vibrations and shocks. To avoid jump, the FRF is analyzed to find the critical values of system parameters and a jump avoidance criterion is introduced.
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Jung, Do Hyun, and Sung In Bae. "Automotive Component Fatigue Life Estimation by Frequency Domain Approach." Key Engineering Materials 297-300 (November 2005): 1776–83. http://dx.doi.org/10.4028/www.scientific.net/kem.297-300.1776.
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Time domain approach with S-N approach and local strain approach were used for fatigue life estimation. But these days, using PSD (Power Spectral Density) method is highlighted, because of short amount of time in measurement and analysis. Especially, PSD method is useful for analysis of fatigue failure which is caused by vibration damage, also FRF (Frequency Response Function) is useful for efficient prediction of fatigue life when the same product is employing different motor vehicle or test condition. In order to estimate fatigue life of compressor for air conditioning, time domain analysis and frequency domain analysis were performed and the results were compared. As a result, results of analysis in frequency domain and time domain were similar. With this, there is recognition of decreasing the period of measuring and analysis in PSD analysis. Moreover, in case of FRF pursued of a part, using FRF is applicable at fatigue life prediction in different testing condition. There was investigated an analysis method with curtailed analysis period by FRF.
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Jia, Jinjie, Yuwen Sun, and Jinbo Niu. "Prediction of Frequency Response Function for Cylindrical Thin-Walled Workpiece with Fixture Support Constraints." Mathematical Problems in Engineering 2021 (August 13, 2021): 1–16. http://dx.doi.org/10.1155/2021/9946310.
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Auxiliary fixtures are widely used to enhance the rigidity of cylindrical thin-walled workpieces (CTWWs) in the machining process. Nevertheless, the accurate and efficient prediction of frequency response function (FRF) for the workpiece-fixture system remains challenging due to the complicated contact constraints between workpiece and fixture. This paper proposes an analytical solution for the comprehensive FRF analysis of the CTWW-fixture system. Firstly, based on the vector mechanics, the mode shape functions of the workpiece are presented using the classical theory of thin shell. The variable separation method is utilized to deal with the inter-mode coupling of the workpiece. Secondly, the motion equation of the CTWW with fixture constraints is established using analytical mechanics from the viewpoint of energy balance. Finally, the FRFs of the CTWW-fixture system are derived by means of modal superposition. Experimental modal tests verify that the predicted FRFs are in good agreement with the measured curves.
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Kim, W.-J., B.-Y. Lee, and Y.-S. Park. "Non-linear joint parameter identification using the frequency response function of the linear substructure." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 218, no. 9 (2004): 947–55. http://dx.doi.org/10.1243/0954406041991314.
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A method based on frequency domain approaches is presented for the non-linear parameter identification of a structure having non-linear joints. The frequency response function (FRF) of the linear substructure, which can be calculated from the finite element method or measured by an experimental method, is used to calculate its FRFs needed in the parameter identification process. This method is easily applicable to a complex real structure having non-linear joints since it uses the FRF of the substructure. Since this method is performed in the frequency domain, the number of equations can be easily increased to as many as required to identify unknown parameters, not only by just varying the excitation amplitude but also by selecting the excitation frequencies. The validity of this method was tested numerically and experimentally with a cantilever beam having a non-linear element. It was verified through examples that the proposed method is useful to identify the non-linear joint parameters of a structure having arbitrary boundaries.
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Susanto, Ari, Setyo Qomarudin Yusuf, Abdul Hamid, Haris Wahyudi, and Subekti Subekti. "IMPLEMENTATION OF FREQUENCY RESPONSE FUNCTION ON TAPPER BEARING MAINTENANCE." SINERGI 23, no. 2 (2019): 132. http://dx.doi.org/10.22441/sinergi.2019.2.006.
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Bearing acts as a pad that supports a shaft to rotate without excessive friction, hold the radial load and maintain the motion towards the left and right shafts (Thrust Load) when turning together. Due to frequent taper bearing damage to the wheels, predictive maintenance is therefore necessary. One of the predictive maintenance methods widely used today is vibration analysis. The principles of vibration-based bearing damage detection using the Frequency Response Function (FRF) method will be shown in this paper. Harmonics signal is given to the bearing surface in a vertical or perpendicular direction to the taper bearing surface. The vibration response measurement was carried out on three axes (x, y, and z). The results of this study indicated the ability of FRFs to predict any damage on the bearing taper.
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Kim, Yong-Su, and Hee-Chang Eun. "Comparison of Damage Detection Methods Depending on FRFs within Specified Frequency Ranges." Advances in Materials Science and Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/5821835.
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Structural damage can be detected using frequency response function (FRF) measured by an impact and the corresponding responses. The change in the mechanical properties of dynamic system for damage detection can seldom be estimated using FRF data extracted from a very limited frequency range. Proper orthogonal modes (POMs) from the FRFs extracted in given frequency ranges and their modified forms can be utilized as damage indices to detect damage. The POM-based damage detection methods must be sensitive to the selected FRFs. This work compares the effectiveness of the damage detection approaches taking the POMs estimated by the FRFs within five different frequency ranges including resonance frequency and antiresonance frequency. It is shown from a numerical example that the POMs extracted from the FRFs within antiresonance frequency ranges provide more explicit information on the damage locations than the ones within resonance frequency ranges.
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Xue, Xiaofeng, Xuefeng Chen, Xingwu Zhang, Baijie Qiao, and Jia Geng. "Hermitian Mindlin Plate Wavelet Finite Element Method for Load Identification." Shock and Vibration 2016 (2016): 1–24. http://dx.doi.org/10.1155/2016/8618202.
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A new Hermitian Mindlin plate wavelet element is proposed. The two-dimensional Hermitian cubic spline interpolation wavelet is substituted into finite element functions to construct frequency response function (FRF). It uses a system’s FRF and response spectrums to calculate load spectrums and then derives loads in the time domain via the inverse fast Fourier transform. By simulating different excitation cases, Hermitian cubic spline wavelets on the interval (HCSWI) finite elements are used to reverse load identification in the Mindlin plate. The singular value decomposition (SVD) method is adopted to solve the ill-posed inverse problem. Compared with ANSYS results, HCSWI Mindlin plate element can accurately identify the applied load. Numerical results show that the algorithm of HCSWI Mindlin plate element is effective. The accuracy of HCSWI can be verified by comparing the FRF of HCSWI and ANSYS elements with the experiment data. The experiment proves that the load identification of HCSWI Mindlin plate is effective and precise by using the FRF and response spectrums to calculate the loads.
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Liu, Xun Tao, Zhao Bo Chen, Li Fu Xu, and Shan Yun Huang. "The Study and Application of Electromagnetic Vibration Shaker Finite Element Model Updating and Validation Technology." Key Engineering Materials 458 (December 2010): 231–36. http://dx.doi.org/10.4028/www.scientific.net/kem.458.231.
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Acording to the fact that the finite element model of electromagnetic vibration shaker for virtual experiment is not accurate enough to complete accurately spacecraft test, made a correlation analysis of the finite element output frequency response function and the measured frequency response function by their correlation coefficients. Analyzed the sensitivity of the materials for FRF and screened the parameters to update, made the correlation coefficient error of electromagnetic vibration shaker finite element model frequency response function and the measured as the optimization objective, the optimization and modification of shaker finite element model parameters were completed by iteration method. The frequency response function of the modified finite element model approximately agreed with the experimental frequency response function. It met the virtual experiments of electromagnetic vibration shaker.
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Vu, Dinh Huong, and Duc Tuan Ta. "Viscous damping estimation of structures using extreme frequency bandwidth method." Vietnam Institute for Building Science and Technology 2024, vi.vol3 (2024): 22–30. https://doi.org/10.59382/j-ibst.2024.vi.vol3-3.
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The classical half-power bandwidth (HPB) method is known as a simple and widely used method to identify damping in experimental research on structural vibrations. However, this method is only effective in systems with small damping and separate natural frequencies. This paper presents the extreme frequency bandwidth (EFB) method and proposes a formula to estimate the viscous damping ratio from the extreme points of the real part of the frequency response function (FRF) in the displacement spectrum analysis of structures. The displacement FRF is obtained by Fourier transform of the simulated load and response signals of the system. The results show that the EFB method can identify the viscous damping in structures that have one or more degrees of freedom with different damping levels.
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Dziedziech, Kajetan, Alexander Nowak, Alexander Hasse, Tadeusz Uhl, and Wiesław J. Staszewski. "Wavelet-based analysis of time-variant adaptive structures." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (2018): 20170245. http://dx.doi.org/10.1098/rsta.2017.0245.
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Wavelet analysis is applied to identify the time-variant dynamics of adaptive structures. The wavelet-based power spectrum of the structural response, wavelet-based frequency response function (FRF) and wavelet-based coherence are used to identify continuously and abruptly varying natural frequencies. A cantilever plate with surface-bonded macro fibre composite—which alters the structural stiffness—is used to demonstrate the application of the methods. The results show that the wavelet-based input–output characteristics—i.e. the FRF and coherence—can identify correctly the dynamics of the analysed time-variant system and reveal the varying natural frequency. The wavelet-based coherence can be used not only for the assessment of the quality of the wavelet-based FRF but also for the identification. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.
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Yin, Hong, Jingjing Ma, Kangli Dong, Zhenrui Peng, Pan Cui, and Chenghao Yang. "Model Updating Method Based on Kriging Model for Structural Dynamics." Shock and Vibration 2019 (April 23, 2019): 1–12. http://dx.doi.org/10.1155/2019/8086024.
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Model updating in structural dynamics has attracted much attention in recent decades. And high computational cost is frequently encountered during model updating. Surrogate model has attracted considerable attention for saving computational cost in finite element model updating (FEMU). In this study, a model updating method using frequency response function (FRF) based on Kriging model is proposed. The optimal excitation point is selected by using modal participation criterion. Initial sample points are chosen via design of experiment (DOE), and Kriging model is built using the corresponding acceleration frequency response functions. Then, Kriging model is improved via new sample points using mean square error (MSE) criterion and is used to replace the finite element model to participate in optimization. Cuckoo algorithm is used to obtain the updating parameters, where the objective function with the minimum frequency response deviation is constructed. And the proposed method is applied to a plane truss model FEMU, and the results are compared with those by the second-order response surface model (RSM) and the radial basis function model (RBF). The analysis results showed that the proposed method has good accuracy and high computational efficiency; errors of updating parameters are less than 0.2%; damage identification is with high precision. After updating, the curves of real and imaginary parts of acceleration FRF are in good agreement with the real ones.
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Kim, Chan-Jung. "Temperature-Dependent Dynamic Characteristics of Carbon-Fiber-Reinforced Plastic for Different Spectral Loading Patterns." Materials 13, no. 22 (2020): 5238. http://dx.doi.org/10.3390/ma13225238.
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The dynamic properties of carbon-fiber-reinforced plastic (CFRP) can be efficiently estimated through a modal damping coefficient and a resonance frequency, and the modal parameters can be calculated using a frequency response function (FRF). The modal parameters used in an CFRP FRF are influenced by the carbon fiber direction, temperature, and spectral loading pattern, as well as the operating conditions. In this study, three parameters—temperature, spectral loading pattern, and carbon fiber direction—were selected as the influential factors for CFRP dynamics, and the sensitivity index formulation was derived from the parameter-dependent FRF of the CFRP structure. The derivatives of the parameter-dependent FRF over the three considered parameters were calculated from the measured modal parameters, and the dynamic sensitivity of the CFRP specimens was explored from the sensitivity index results for five different directional CFRP specimens. The acceleration response of a simple CFRP specimen was obtained via a uniaxial excitation test at temperatures ranging from −8 to 105 °C for the following two spectral loading cases: harmonic and random.
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Shen, Xue Jing, Jiao Xia Lan, Xiao Rong Yang, and Fang Ji. "Modal Analysis of Laminated Composite Beams Based on Elastic Wave Theory." Applied Mechanics and Materials 151 (January 2012): 275–80. http://dx.doi.org/10.4028/www.scientific.net/amm.151.275.
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The reverberation ray matrix method (MRRM) for analyzing dynamic response of elastic trusses is extended and used to solve the natural frequency and vibration mode of laminated beams. In this study, the MRRM is employed to obtain the frequency response function (FRF) of displacement of a laminated beam under the action of a unit impulse load. The natural frequencies are determined from the peak of the curve of FRF when a resonant frequency is approached. And the mode is retrieved from the ad joint matrix of the coefficient matrix of the governing equations of MRRM. The accuracy of result of MRRM is verified by a simply supported symmetrically laminated beam compared with the analytical solution of classical theory, which is also proved by finite element method (FEM).
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Wen, Kun Long, and Hou Jun Qi. "Predicting Tool Point FRF by RCSA in High Speed Milling." Advanced Materials Research 1006-1007 (August 2014): 398–402. http://dx.doi.org/10.4028/www.scientific.net/amr.1006-1007.398.
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Tool point frequency response function (FRF) is the key parameters to predict the milling stability in high-speed milling. Receptance coupling substructure analysis (RCSA) is described to predict the tool point FRF. The major difficulties in RCSA are the identification of joint connection parameters and the obtaining of FRFs of substructure. This paper separation of the milling system into three substructures: the machine-spindle-holder taper, the extended holder-tool shank, and the tool extended portion. Develop the connection model compose of linear and rotational springs and dampers. Determine the substructure FRF by measurement and Euler-Bernoulli beam model. Tool point FRF is obtained by coupling the substructure FRFs through the connection model by RCSA.
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Khiem, Nguyen Tien, Tran Thanh Hai, Le Khanh Toan, Nguyen Thi Lan, and Ho Quang Quyet. "A novel criterion for crack detection in beam structures by frequency response functions." Vietnam Journal of Mechanics 45, no. 3 (2023): 273–86. http://dx.doi.org/10.15625/0866-7136/19040.
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The frequency response function (FRF) is a fruitful attribute that includes almost all dynamical characteristics of a structure such as natural frequencies and modes, damping coefficients, or resonance and antiresonance conceptions. However, the complex feature of FRF has not been thoroughly employed for structural damage detection. In the present study, a novel indicator extracted from FRFs of beam structures is developed for crack identification. The damage indicator originated from the well-known mode assurance criterion (MAC) and therefore it is termed spectral assurance criterion (SAC). First, a coherence coefficient calculated from FRFs of intact and damaged beams and called herein spectral damage index (SDI) is analyzed for examining sensitivity of FRFs to crack. Then, SAC calculated for different FRFs of the same damaged structure is employed for crack detection by the so-called contour method. Results obtained in numerical examples of the crack detection problem show that SAC is really a novel and efficient criterion for crack identification in beams from measured FRFs.
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Liu, C. Q., and C. C. Chang. "A method for vibration absorber tuning based on baseline frequency response functions." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 221, no. 9 (2007): 1071–78. http://dx.doi.org/10.1243/09544070jauto64.
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This paper presents explicit expressions for new frequency response functions (FRFs) of a primary system when a vibration absorber is attached to it. The new FRF is expressed in terms of the baseline (‘old’) FRFs of the primary system and the physical parameters (the mass, stiffness, and damping) of the vibration absorber. The baseline FRF of the primary system can be obtained by either analytical or experimental methods. This approach allows engineers and designers to evaluate a number of alternative vibration absorbers before these absorbers are physically implemented on the structure. Therefore a considerable amount of time and effort for engineers and designers can be saved. Several examples are provided to illustrate the use of the method.
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Chen, Shilei, Zhi Chao Ong, Wei Haur Lam, Kok-Sing Lim, and Khin Wee Lai. "Unsupervised Damage Identification Scheme Using PCA-Reduced Frequency Response Function and Waveform Chain Code Analysis." International Journal of Structural Stability and Dynamics 20, no. 08 (2020): 2050091. http://dx.doi.org/10.1142/s0219455420500911.
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Mechanical machines face structural damage problems during their service life. Structural damage can severely affect safety and functionality of the structure and lead to economic loss. In this work, a damage identification scheme is developed by combining waveform chain code (WCC) analysis and hierarchical cluster analysis based on complex network theory. Waveform chain code analysis was carried out using the principal component analysis reduced frequency response function (PCA-reduced FRF), and the areas under the slope differential value curves were calculated as damage-sensitive WCC features. Unsupervised machine learning using hierarchical cluster analysis was then conducted on these damage-sensitive features. A rectangular Perspex plate was studied using the newly developed damage identification scheme as an example. Experimental results showed that the proposed scheme can successfully separate all the damage conditions from the undamaged state with 100% accuracy. In terms of damage severity and location identification, the proposed scheme is sensitive to detect damage severity with damage index as low as 0.17. In addition, combination of PCA-reduced FRF and mode shapes showed positive correlation between the magnitude of the resonant peak and the displacement of the impact point in identifying different damage locations of the plate.