Academic literature on the topic 'Euler Beam Theory'
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Journal articles on the topic "Euler Beam Theory"
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LIM, TEIK-CHENG. "ANALYSIS OF AUXETIC BEAMS AS RESONANT FREQUENCY BIOSENSORS." Journal of Mechanics in Medicine and Biology 12, no. 05 (December 2012): 1240027. http://dx.doi.org/10.1142/s0219519412400271.
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The mechanics of beam vibration is of fundamental importance in understanding the shift of resonant frequency of microcantilever and nanocantilever sensors. Unlike the simpler Euler–Bernoulli beam theory, the Timoshenko beam theory takes into consideration rotational inertia and shear deformation. For the case of microcantilevers and nanocantilevers, the minute size, and hence low mass, means that the topmost deviation from the Euler–Bernoulli beam theory to be expected is shear deformation. This paper considers the extent of shear deformation for varying Poisson's ratio of the beam material, with special emphasis on solids with negative Poisson's ratio, which are also known as auxetic materials. Here, it is shown that the Timoshenko beam theory approaches the Euler–Bernoulli beam theory if the beams are of solid cross-sections and the beam material possess high auxeticity. However, the Timoshenko beam theory is significantly different from the Euler–Bernoulli beam theory for beams in the form of thin-walled tubes regardless of the beam material's Poisson's ratio. It is herein proposed that calculations on beam vibration can be greatly simplified for highly auxetic beams with solid cross-sections due to the small shear correction term in the Timoshenko beam deflection equation.
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Gul, U., and M. Aydogdu. "Wave Propagation Analysis in Beams Using Shear Deformable Beam Theories Considering Second Spectrum." Journal of Mechanics 34, no. 3 (May 15, 2017): 279–89. http://dx.doi.org/10.1017/jmech.2017.27.
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AbstractIn this study, wave propagation in beams is studied using different beam theories like Euler-Bernoulli, Timoshenko and Reddy beam theories. Dispersion curves obtained for these beam theories are compared with the exact plane elasticity solutions. It is obtained that, there are two branches for Reddy beam theory similar to the Timoshenko beam theory. However, one branch is obtained for Euler-Bernoulli beam theory. The effects of in-plane load on Timoshenko and Reddy beam theories are examined and dispersion curves of the Timoshenko and Reddy beams are compared with exact plane elasticity solution. In Timoshenko beam theory, qualitative difference between the two spectrums has been lost with in-plane loads for some wave numbers.
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Siva Sankara Rao, Yemineni, Kutchibotla Mallikarjuna Rao, and V. V. Subba Rao. "Estimation of damping in riveted short cantilever beams." Journal of Vibration and Control 26, no. 23-24 (March 20, 2020): 2163–73. http://dx.doi.org/10.1177/1077546320915313.
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In layered and riveted structures, vibration damping happens because of a micro slip that occurs because of a relative motion at the common interfaces of the respective jointed layers. Other parameters that influence the damping mechanism in layered and riveted beams are the amplitude of initial excitation, overall length of the beam, rivet diameter, overall beam thickness, and many layers. In this investigation, using the analytical models such as the Euler–Bernoulli beam theory and Timoshenko beam theory and half-power bandwidth method, the free transverse vibration analysis of layered and riveted short cantilever beams is carried out for observing the damping mechanism by estimating the damping ratio, and the obtained results from the Euler–Bernoulli beam theory and Timoshenko beam theory analytical models are validated by the half-power bandwidth method. Although the Euler–Bernoulli beam model overestimates the damping ratio value by a very less fraction, both the models can be used to evaluate damping for short riveted cantilever beams along with the half-power bandwidth method.
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Ključanin, Dino, and Abaz Manđuka. "The cantilever beams analysis by the means of the first-order shear deformation and the Euler-Bernoulli theory." Tehnički glasnik 13, no. 1 (March 23, 2019): 63–67. http://dx.doi.org/10.31803/tg-20180802210608.
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The effect of the Timoshenko theory and the Euler-Bernoulli theory are investigated in this paper through numerical and analytical analyses. The investigation was required to obtain the optimized position of the pipes support. The Timoshenko beam theory or the first order shear deformation theory was used regarding thick beams where the shearing effect of the beam is considered. The study of the thin beams was performed with the Euler-Bernoulli theory. The analysis was done for stainless steel AISI-440C beams with the rectangular cross-section. The steel beams were a cantilever and stressed under varying point-centred load.
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Li, Anqing, Qing Wang, Ming Song, Jun Chen, Weiguang Su, Shasha Zhou, and Li Wang. "On Strain Gradient Theory and Its Application in Bending of Beam." Coatings 12, no. 9 (September 5, 2022): 1304. http://dx.doi.org/10.3390/coatings12091304.
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The general strain gradient theory of Mindlin is re-visited on the basis of a new set of higher-order metrics, which includes dilatation gradient, deviatoric stretch gradient, symmetric rotation gradient and curvature. A strain gradient bending theory for plane-strain beams is proposed based on the present strain gradient theory. The stress resultants are re-defined and the corresponding equilibrium equations and boundary conditions are derived for beams. The semi-inverse solution for a pure bending beam is obtained and the influence of the Poisson’s effect and strain gradient components on bending rigidity is investigated. As a contrast, the solution of the Bernoulli–Euler beam is also presented. The results demonstrate that when Poisson’s effect is ignored, the result of the plane-strain beam is consistent with that of the Bernoulli–Euler beam in the couple stress theory. While for the strain gradient theory, the bending rigidity of a plane-strain beam ignoring the Poisson’s effect is smaller than that of the Bernoulli–Euler beam due to the influence of the dilatation gradient and the deviatoric stretch gradient along the thickness direction of the beam. In addition, the influence of a strain gradient along the length direction on a bending rigidity is negligible.
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Golushko, Sergey, Gleb Gorynin, and Arseniy Gorynin. "Analytic solutions for free vibration analysis of laminated beams in three-dimensional statement." EPJ Web of Conferences 221 (2019): 01012. http://dx.doi.org/10.1051/epjconf/201922101012.
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In this research we consider free vibrations of laminated beams in terms of three-dimensional linear theory of elasticity. Analytic solutions for natural frequencies of laminated beams are obtained by using an asymptotic splitting method. The results were compared with classical Euler“Bernoulli beam theory and Timoshenko beam theory.
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Wang, Gang. "Analysis of bimorph piezoelectric beam energy harvesters using Timoshenko and Euler–Bernoulli beam theory." Journal of Intelligent Material Systems and Structures 24, no. 2 (September 27, 2012): 226–39. http://dx.doi.org/10.1177/1045389x12461080.
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Single-degree-of-freedom lumped parameter model, conventional finite element method, and distributed parameter model have been developed to design, analyze, and predict the performance of piezoelectric energy harvesters with reasonable accuracy. In this article, a spectral finite element method for bimorph piezoelectric beam energy harvesters is developed based on the Timoshenko beam theory and the Euler–Bernoulli beam theory. Linear piezoelectric constitutive and linear elastic stress/strain models are assumed. Both beam theories are considered in order to examine the validation and applicability of each beam theory for a range of harvester sizes. Using spectral finite element method, a minimum number of elements is required because accurate shape functions are derived using the coupled electromechanical governing equations. Numerical simulations are conducted and validated using existing experimental data from the literature. In addition, parametric studies are carried out to predict the performance of a range of harvester sizes using each beam theory. It is concluded that the Euler–Bernoulli beam theory is sufficient enough to predict the performance of slender piezoelectric beams (slenderness ratio > 20, that is, length over thickness ratio > 20). In contrast, the Timoshenko beam theory, including the effects of shear deformation and rotary inertia, must be used for short piezoelectric beams (slenderness ratio < 5).
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Naghinejad, Maysam, and Hamid Reza Ovesy. "Free vibration characteristics of nanoscaled beams based on nonlocal integral elasticity theory." Journal of Vibration and Control 24, no. 17 (June 28, 2017): 3974–88. http://dx.doi.org/10.1177/1077546317717867.
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In the present article, the total potential energy principle and the nonlocal integral elasticity theory have been used to develop a novel finite element method for studying the free vibration behavior of nano-scaled beams. The formulations are based on Euler-Bernoulli beam theory and this method is able to properly analyze the free vibration of beams with various boundary conditions. By implementing the variational statements, the eigenvalue problem of the free vibration is obtained. The validation investigation is pursued by comparing the results of the current study with those available in the literature. The effects of nonlocal parameter, geometry parameters and boundary conditions on the free vibration of the Euler-Bernoulli beam are then studied.
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Shimpi, Rameshchandra P., Rajesh A. Shetty, and Anirban Guha. "A simple single variable shear deformation theory for a rectangular beam." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 24 (September 29, 2016): 4576–91. http://dx.doi.org/10.1177/0954406216670682.
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This paper proposes a simple single variable shear deformation theory for an isotropic beam of rectangular cross-section. The theory involves only one fourth-order governing differential equation. For beam bending problems, the governing equation and the expressions for the bending moment and shear force of the theory are strikingly similar to those of Euler–Bernoulli beam theory. For vibration and buckling problems, the Euler–Bernoulli beam theory governing equation comes out as a special case when terms pertaining to the effects of shear deformation are ignored from the governing equation of present theory. The chosen displacement functions of the theory give rise to a realistic parabolic distribution of transverse shear stress across the beam cross-section. The theory does not require a shear correction factor. Efficacy of the proposed theory is demonstrated through illustrative examples for bending, free vibrations and buckling of isotropic beams of rectangular cross-section. The numerical results obtained are compared with those of exact theory (two-dimensional theory of elasticity) and other first-order and higher-order shear deformation beam theory results. The results obtained are found to be accurate.
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Karaoglu, P., and M. Aydogdu. "On the forced vibration of carbon nanotubes via a non-local Euler—Bernoulli beam model." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 2 (February 1, 2010): 497–503. http://dx.doi.org/10.1243/09544062jmes1707.
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This article studies the forced vibration of the carbon nanotubes (CNTs) using the local and the non-local Euler—Bernoulli beam theory. Amplitude ratios for the local and the non-local Euler—Bernoulli beam models are given for single- and double-walled CNTs. It is found that the non-local models give higher amplitudes when compared with the local Euler—Bernoulli beam models. The non-local Euler—Bernoulli beam model predicts lower resonance frequencies.
Dissertations / Theses on the topic "Euler Beam Theory"
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Batihan, Ali Cagri. "Vibration Analysis Of Cracked Beams On Elastic Foundation Using Timoshenko Beam Theory." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613602/index.pdf.
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In this thesis, transverse vibration of a cracked beam on an elastic foundation and
the effect of crack and foundation parameters on transverse vibration natural
frequencies are studied. Analytical formulations are derived for a beam with
rectangular cross section. The crack is an open type edge crack placed in the
medium of the beam and it is uniform along the width of the beam. The cracked
beam rests on an elastic foundation. The beam is modeled by two different beam
theories, which are Euler-Bernoulli beam theory and Timoshenko beam theory.
The effect of the crack is considered by representing the crack by rotational
springs. The compliance of the spring that represents the crack is obtained by
using fracture mechanics theories. Different foundation models are discussedthese models are Winkler Foundation, Pasternak Foundation, and generalized foundation. The equations of motion are derived by applying Newton'
s 2nd law on an infinitesimal beam element. Non-dimensional parameters are introduced into equations of motion. The beam is separated into pieces at the crack location. By applying the compatibility conditions at the crack location and boundary conditions, characteristic equation whose roots give the non-dimensional natural frequencies is obtained. Numerical solutions are done for a beam with square cross sectional area. The effects of crack ratio, crack location and foundation parameters on transverse vibration natural frequencies are presented. It is observed that existence of crack reduces the natural frequencies. Also the elastic foundation increases the stiffness of the system thus the natural frequencies. The natural frequencies are also affected by the location of the crack.
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Ho, Qhinhon D. "An Assessment Of The Accuracy Of The Euler-Bernoulli Beam Theory For Calculating Strain and Deflection in Composite Sandwich Beams." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2084.
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This study focuses on assessing the accuracy of the Euler-Bernoulli beam theory as computational bases to calculate strain and deflection of composite sandwich beam subjected to three-point and four-point bending. Two groups of composite sandwich beams tests results will be used for comparison purposes. Mechanical properties for the laminated skin are provided by researchers from University of Mississippi (Ellen Lackey et al., 2000). Mechanical properties for the balsa wood core are provided by Alcan Baltek Corporation. Appropriate material properties and test geometries are then used in the Euler-Bernoulli-based algorithm in order to generate analytical data for comparison to experimental data provided by researchers from University of New Orleans (UNO, 2005). The resulting single material cross section is then analyzed in the traditional manner using the Euler-Bernoulli beam theory. In general, the Euler-Bernoulli beam theory provides an appropriate analytical approach in predicting flexural behavior of composite sandwich beams.
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Pratt, Brittan Sheldon. "An assessment of least squares finite element models with applications to problems in heat transfer and solid mechanics." Texas A&M University, 2008. http://hdl.handle.net/1969.1/85941.
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Research is performed to assess the viability of applying the least squares model
to one-dimensional heat transfer and Euler-Bernoulli Beam Theory problems. Least
squares models were developed for both the full and mixed forms of the governing
one-dimensional heat transfer equation along weak form Galerkin models. Both least
squares and weak form Galerkin models were developed for the first order and second
order versions of the Euler-Bernoulli beams.
Several numerical examples were presented for the heat transfer and Euler-
Bernoulli beam theory. The examples for heat transfer included: a differential equation having the same form as the governing equation, heat transfer in a fin, heat
transfer in a bar and axisymmetric heat transfer in a long cylinder. These problems
were solved using both least squares models, and the full form weak form Galerkin
model. With all four examples the weak form Galerkin model and the full form least
squares model produced accurate results for the primary variables. To obtain accurate results with the mixed form least squares model it is necessary to use at least
a quadratic polynominal. The least squares models with the appropriate approximation functions yielde more accurate results for the secondary variables than the weak
form Galerkin.
The examples presented for the beam problem include: a cantilever beam with
linearly varying distributed load along the beam and a point load at the end, a simply
supported beam with a point load in the middle, and a beam fixed on both ends with a distributed load varying cubically. The first two examples were solved using the
least squares model based on the second order equation and a weak form Galerkin
model based on the full form of the equation. The third problem was solved with
the least squares model based on the second order equation. Both the least squares
model and the Galerkin model calculated accurate results for the primary variables,
while the least squares model was more accurate on the secondary variables.
In general, the least-squares finite element models yield more acurate results for
gradients of the solution than the traditional weak form Galkerkin finite element models. Extension of the present assessment to multi-dimensional problems and nonlinear
provelms is awaiting attention.
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Dettmann, Aaron. "Loosely coupled, modular framework for linear static aeroelastic analyses." Thesis, KTH, Lättkonstruktioner, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-262047.
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A computational framework for linear static aeroelastic analyses is presented. The overall aeroelasticity model is applicable to conceptual aircraft design studies and other low-fidelity aero-structural analyses. A partitioned approach is used, i. e. separate solvers for aerodynamics and structure analyses are coupled in a suitable way, together forming a model for aeroelastic simulations. Aerodynamics are modelled using the vortexlattice method (VLM), a simple computational fluid dynamics (CFD) model based on potential flow. The structure is represented by a three-dimensional (3D) Euler-Bernoulli beam model in a finite element method (FEM) formulation. A particular focus was put on the modularity and loose coupling of aforementioned models. The core of the aeroelastic framework was abstracted, such that it does not depend on any specific details of the underlying aerodynamics and structure modules. The final aeroelasticity model constitutes independent software tools for the VLM and the beam FEM, as well as a framework enabling the aeroelastic coupling. These different tools have been developed as part of this thesis work. A wind tunnel experiment with a simple wing model is presented as a validation test case. An aero-structural analysis of a fully elastic unmanned aerial vehicle (UAV) (OptiMale) is described and results are compared with an existing higherfidelity study.Rapporten beskriver en beräkningsmodell för linjära, statisk aeroelastiska analyser. Modellen kan användas för konceptuella designstudier av flygplan. En partitionerad metod används, d v s separata lösare för aerodynamik- och strukturanalyser kopplas på ett lämpligt sätt, och bildar tillsammans en modell för aeroelastiska simulationer. Aerodynamik modelleras med hjälp av en så kallad vortex-lattice method (VLM), en enkel modell för beräkningsströmningsdynamik (CFD) som är baserad på friktionsfri strömning. Strukturen representeras av en tredimensionell (3D) Euler-Bernoulli-balkmodell implementerad med hjälp av en finita elementmetod (FEM). Ovannämnda modeller har utvecklats med fokus på modularitet och lös koppling. Kärnan i den aeroelastiska modellen har abstraherats så att den inte beror på specifika detaljer i de underliggande aerodynamik- och strukturmodulerna. Aeroelasticitetsmodellen i sin helhet består av separata mjukvaruprogram för VLM och balk-FEM, såväl som ett ramverk som möjliggör den aeroelastiska kopplingen. Dessa olika program har utvecklats som en del av examensarbetet. Ett vindtunnelförsök med en enkel vingmodell presenteras som ett valideringstest. Dessutom beskrivs en analys av ett elastiskt obemannad flygplan (OptiMale) och resultaten jämförs med en befintlig studie som har genomförts med modeller av högre trovärdighet.
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Dona, Marco. "Static and dynamic analysis of multi-cracked beams with local and non-local elasticity." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/14893.
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The thesis presents a novel computational method for analysing the static and dynamic behaviour of a multi-damaged beam using local and non-local elasticity theories. Most of the lumped damage beam models proposed to date are based on slender beam theory in classical (local) elasticity and are limited by inaccuracies caused by the implicit assumption of the Euler-Bernoulli beam model and by the spring model itself, which simplifies the real beam behaviour around the crack. In addition, size effects and material heterogeneity cannot be taken into account using the classical elasticity theory due to the absence of any microstructural parameter. The proposed work is based on the inhomogeneous Euler-Bernoulli beam theory in which a Dirac's delta function is added to the bending flexibility at the position of each crack: that is, the severer the damage, the larger is the resulting impulsive term. The crack is assumed to be always open, resulting in a linear system (i.e. nonlinear phenomena associated with breathing cracks are not considered). In order to provide an accurate representation of the structure's behaviour, a new multi-cracked beam element including shear effects and rotatory inertia is developed using the flexibility approach for the concentrated damage. The resulting stiffness matrix and load vector terms are evaluated by the unit-displacement method, employing the closed-form solutions for the multi-cracked beam problem. The same deformed shapes are used to derive the consistent mass matrix, also including the rotatory inertia terms. The two-node multi-damaged beam model has been validated through comparison of the results of static and dynamic analyses for two numerical examples against those provided by a commercial finite element code. The proposed model is shown to improve the computational efficiency as well as the accuracy, thanks to the inclusion of both shear deformations and rotatory inertia. The inaccuracy of the spring model, where for example for a rotational spring a finite jump appears on the rotations' profile, has been tackled by the enrichment of the elastic constitutive law with higher order stress and strain gradients. In particular, a new phenomenological approach based upon a convenient form of non-local elasticity beam theory has been presented. This hybrid non-local beam model is able to take into account the distortion on the stress/strain field around the crack as well as to include the microstructure of the material, without introducing any additional crack related parameters. The Laplace's transform method applied to the differential equation of the problem allowed deriving the static closed-form solution for the multi-cracked Euler-Bernoulli beams with hybrid non-local elasticity. The dynamic analysis has been performed using a new computational meshless method, where the equation of motions are discretised by a Galerkin-type approximation, with convenient shape functions able to ensure the same grade of approximation as the beam element for the classical elasticity. The importance of the inclusion of microstructural parameters is addressed and their effects are quantified also in comparison with those obtained using the classical elasticity theory.
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Dixit, Akash. "Damage modeling and damage detection for structures using a perturbation method." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/43575.
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This thesis is about using structural-dynamics based methods to address the existing challenges in the field of Structural Health Monitoring (SHM). Particularly, new structural-dynamics based methods are presented, to model areas of damage, to do damage diagnosis and to estimate and predict the sensitivity of structural vibration properties like natural frequencies to the presence of damage.
Towards these objectives, a general analytical procedure, which yields nth-order expressions governing mode shapes and natural frequencies and for damaged elastic structures such as rods, beams, plates and shells of any shape is presented. Features of the procedure include the following:
1. Rather than modeling the damage as a fictitious elastic element or localized or global change in constitutive properties, it is modeled in a mathematically rigorous manner as a geometric discontinuity.
2. The inertia effect (kinetic energy), which, unlike the stiffness effect (strain energy), of the damage has been neglected by researchers, is included in it.
3. The framework is generic and is applicable to wide variety of engineering structures of different shapes with arbitrary boundary conditions which constitute self adjoint systems and also to a wide variety of damage profiles and even multiple areas of damage.
To illustrate the ability of the procedure to effectively model the damage, it is applied to beams using Euler-Bernoulli and Timoshenko theories and to plates using Kirchhoff's theory, supported on different types of boundary conditions. Analytical results are compared with experiments using piezoelectric actuators and non-contact Laser-Doppler Vibrometer sensors.
Next, the step of damage diagnosis is approached. Damage diagnosis is done using two methodologies. One, the modes and natural frequencies that are determined are used to formulate analytical expressions for a strain energy based damage index. Two, a new damage detection parameter are identified.
Assuming the damaged structure to be a linear system, the response is expressed as the summation of the responses of the corresponding undamaged structure and the response (negative response) of the damage alone. If the second part of the response is isolated, it forms what can be regarded as the damage signature. The damage signature gives a clear indication of the damage. In this thesis, the existence of the damage signature is investigated when the damaged structure is excited at one of its natural frequencies and therefore it is called ``partial mode contribution". The second damage detection method is based on this new physical parameter as determined using the partial mode contribution. The physical reasoning is verified analytically, thereupon it is verified using finite element models and experiments. The limits of damage size that can be determined using the method are also investigated. There is no requirement of having a baseline data with this damage detection method. Since the partial mode contribution is a local parameter, it is thus very sensitive to the presence of damage. The parameter is also shown to be not affected by noise in the detection ambience.
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Gonzalez, Campos David Jonathan. "A Study of Shock Analysis Using the Finite Element Method Verified with Euler-Bernoulli Beam Theory; Mechanical Effects Due to Pulse Width Variation of Shock Inputs; and Evaluation of Shock Response of a Mixed Flow Fan." DigitalCommons@CalPoly, 2014. https://digitalcommons.calpoly.edu/theses/1294.
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A Study Of Shock Analysis Using The Finite Element Method Verified With Euler-Bernoulli Beam Theory; Mechanical Effects Due To Pulse Width Variation Of Shock Inputs; And Evaluation Of Shock Response Of A Mixed Flow Fan
David Jonathan González Campos
For many engineers that use finite element analysis or FEA, it is very important to know how to properly model and obtain accurate solutions for complicated loading conditions such as shock loading. Transient acceleration loads, such as shocks, are not as common as static loads. Analyzing these types of problems is less understood, which is the basis for this study. FEA solutions are verified using classical theory, as well as experimental results. The complex loading combination of shock and high speed rotation is also studied. Ansys and its graphic user interface, Workbench Version 14.5, are the programs used to solve these types of problems. Classical theory and Matlab codes, as well as experimental results, are used to verify finite element solutions for a simple structure, such as a cantilevered beam. The discrepancy of these FEA results is found to be 2.3%. The Full Method and the Mode Superposition Method in Ansys are found to be great solution tools for shock loading conditions, including complex acceleration and force conditions. The Full Method requires less pre-processing but solutions could take days, as opposed to hours, to complete in comparison with the Mode Superposition Method, depending on the 3D Model. The Mode Superposition Method requires more time and input by the user but solves relatively quickly. Furthermore, a new representation of critical pulse width of the shock inputs is presented. Experimental and finite element analyses of a complete mixed flow fan undergoing ballistic shock is also completed; deformation results due to shock loading, combined with rotation and aerodynamic loading, account for 32.3% of the total deformation seen from experimental testing. Solution methods incorporated in Ansys, and validation of FEA results using theory, have great potential implications as powerful tools for engineering students and practicing engineers.
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Chidurala, Manohar. "Dynamic Characteristics of Biologically Inspired Hair Receptors for Unmanned Aerial Vehicles." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2040.
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The highly optimized performance of nature’s creations and biological assemblies has inspired the development of their engineered counter parts that can potentially outperform conventional systems. In particular, bat wings are populated with air flow hair receptors which feedback the information about airflow over their surfaces for enhanced stability and maneuverability during their flight. The hairs in the bat wing membrane play a role in the maneuverability tasks, especially during low-speed flight. The developments of artificial hair sensors (AHS) are inspired by biological hair cells in aerodynamic feedback control designs. Current mathematical models for hair receptors are limited by strict simplifying assumptions of creeping flow hair Reynolds number on AHS fluid-structure interaction (FSI), which may be violated for hair structures integrated on small-scaled Unmanned Aerial Vehicles (UAVs). This study motivates by an outstanding need to understand the dynamic response of hair receptors in flow regimes relevant to bat-scaled UAVs. The dynamic response of the hair receptor within the creeping flow environment is investigated at distinct freestream velocities to extend the applicability of AHS to a wider range of low Reynolds number platforms. Therefore, a threedimensional FSI model coupled with a finite element model using the computational fluid dynamics (CFD) is developed for a hair-structure and multiple hair-structures in the airflow. The Navier-Stokes equations including continuity equation are solved numerically for the CFD model. The grid independence of the FSI solution is studied from the simulations of the hairstructure mesh and flow mesh around the hair sensor. To describe the dynamic response of the hair receptors, the natural frequencies and mode shapes of the hair receptors, computed from the finite element model, are compared with the excitation frequencies in vacuum. This model is described with both the boundary layer effects and effects of inertial forces due to fluid-structure xiv interaction of the hair receptors. For supporting the FSI model, the dynamic response of the hair receptor is also validated considering the Euler-Bernoulli beam theory including the steady and unsteady airflow.
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Belkhiri, Ayman. "Modélisation dynamique de la locomotion compliante : Application au vol battant bio-inspiré de l'insecte." Phd thesis, Ecole des Mines de Nantes, 2013. http://tel.archives-ouvertes.fr/tel-00874497.
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Le travail présenté dans cette thèse est consacré à la modélisation de la dynamique de locomotion des "soft robots", i.e. les systèmes multi-corps mobiles compliants. Ces compliances peuvent être localisées et considérées comme des liaisons passives du système,ou bien introduites par des flexibilités distribuées le long des corps. La dynamique de ces systèmes est modélisée en adoptant une approche Lagrangienne basée sur les outils mathématiques développés par l'école américaine de mécanique géométrique. Du point de vue algorithmique, le calcul de ces modèles dynamiques s'appuie sur un algorithme récursif et efficace de type Newton-Euler, ici étendu aux robots locomoteurs munis d'organes compliants. Poursuivant des objectifs de commande et de simulation rapide pour la robotique, l'algorithme proposé est capable de résoudre la dynamique externe directe ainsi que la dynamique inverse des couples internes. Afin de mettre en pratique l'ensemble de ces outils de modélisation, nous avons pris le vol battant des insectes comme exemple illustratif. Les équations non-linéaires qui régissent les déformations passives de l'aile sont établies en appliquant deux méthodes différentes. La première consiste à séparer le mouvement de l'aile en une composante rigide dite de "repère flottant" et une composante de déformation. Cette dernière est paramétrée dans le repère flottant par la méthode des modes supposés ici appliquée à l'aile vue comme une poutre d'Euler-Bernoulli soumise à la flexion et à la torsion. Quant à la seconde approche, les mouvements de l'aile n'y sont pas séparés mais directement paramétrés par les transformations finies rigides et absolues d'une poutre Cosserat. Cette approche est dite Galiléenne ou "géométriquement exacte" en raison du fait qu'elle ne requiert aucune approximation en dehors des inévitables discrétisations spatiale et temporelle imposées parla résolution numérique de la dynamique du vol. Dans les deux cas,les forces aérodynamiques sont prises en compte via un modèle analytique simplifié de type Dickinson. Les modèles et algorithmes résultants sont appliqués à la conception d'un simulateur du vol, ainsi qu'à la conception d'un prototype d'aile, dans le contexte du projet coopératif (ANR) EVA.
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Johnson, William Richard. "Active Structural Acoustic Control of Clamped and Ribbed Plates." BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/4011.
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A control metric, the weighted sum of spatial gradients (WSSG), has been developed for use in active structural acoustic control (ASAC). Previous development of WSSG [1] showed that it was an effective control metric on simply supported plates, while being simpler to measure than other control metrics, such as volume velocity. The purpose of the current work is to demonstrate that the previous research can be generalized to plates with a wider variety of boundary conditions and on less ideal plates. Two classes of plates have been considered: clamped flat plates, and ribbed plates. On clamped flat plates an analytical model has been developed for use in WSSG that assumes the mode shapes are the product of clamped-clamped beam mode shapes. The boundary condition specific weights for use in WSSG have been derived from this formulation and provide a relatively uniform measurement field, as in the case of the simply supported plate. Using this control metric, control of radiated sound power has been simulated. The results show that WSSG provides comparable control to volume velocity on the clamped plate. Results also show, through random placement of the sensors on the plate, that similar control can be achieved regardless of sensor location. This demonstrates that WSSG is an effective control metric on a variety of boundary conditions. Ribbed plates were considered because of their wide use in aircraft and ships. In this case, a finite-element model of the plate has been used to obtain the displacement field on the plate under a variety of boundary conditions. Due to the discretized model involved, a numerical, as opposed to analytical, formulation for WSSG has been developed. Simulations using this model show that ASAC can be performed effectively on ribbed plates. In particular WSSG was found to perform comparable to or better than volume velocity on all boundary conditions examined. The sensor insensitivity property was found to hold within each section (divided by the ribs) of the plate, a slightly modified form of the flat plate insensitivity property where the plates have been shown to be relatively insensitive to sensor location over the entire surface of the plate. Improved control at natural frequencies can be achieved by applying a second control force. This confirms that ASAC is a viable option for the control of radiated sound power on non-ideal physical systems similar to ribbed plates.
Book chapters on the topic "Euler Beam Theory"
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Bauchau, O. A., and J. I. Craig. "Euler-Bernoulli beam theory." In Structural Analysis, 173–221. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2516-6_5.
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Öchsner, Andreas. "Euler–Bernoulli Beam Theory." In Classical Beam Theories of Structural Mechanics, 7–66. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76035-9_2.
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Krey, Maximilian, and Hannes Töpfer. "Topology Optimization of Magnetoelectric Sensors Using Euler-Bernoulli Beam Theory." In Microactuators, Microsensors and Micromechanisms, 115–24. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61652-6_10.
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Prajapati, S. K., V. K. Gupta, and S. Mukherjee. "Mathematical Modelling of Stepped Beam Energy Harvesting Using Euler–Bernoulli’s Theory." In Springer Proceedings in Physics, 549–65. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78919-4_43.
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Kim, Cheol Woong, Sang Heon Lee, and Kee Joo Kim. "Modified Bernoulli-Euler Laminate Beam Theory Using Total Effective Moment in LIPCA." In Advances in Composite Materials and Structures, 413–16. Stafa: Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-427-8.413.
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Cauvin, Aldo, and Giuseppe Stagnitto. "L. Euler and the birth of modern structural mechanics. From the catenary to the beam theory." In Studies in History of Mathematics Dedicated to A.P. Youschkevitch, 217–34. Turnhout: Brepols Publishers, 2002. http://dx.doi.org/10.1484/m.dda-eb.4.01017.
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Zhang, Jianxun, Pengchong Zhang, Huicun Song, and Lei Zhu. "Transverse Vibration Characteristics of Clamped-Elastic Pinned Beam Under Compressive Axial Loads." In Advances in Frontier Research on Engineering Structures, 527–39. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-8657-4_47.
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AbstractBased on the Bernoulli–Euler theory, the vibration characteristics of a clamped-elastic pinned beam under the elastic constraint and the compressive axial loads are derived and verified by finite element method. The results of examples show that the natural frequency of the beam decreases with loads increase and the frequency increases with the increase of the elastic constraint stiffness. When the constraint stiffness increases from 104 to 108 N/m, the first-order natural frequency becomes 4.24 times, the second-order natural frequency becomes 2.19 times, and the third-order natural frequency becomes 1.57 times; when the constraint is weak, the loads change is mainly reflected in the first mode shape. When the constraint stiffness is 104 N/m, the first-order natural frequency decreases by 20%, the second-order modal natural frequency changes by 3%, and the third-order natural frequency changes by less than 1%. The range of the elastic constraints with significant changes in the natural frequencies of the higher-order modes is larger. When the first-order frequency is taken to 100EI/l3, the change tends to be flat, the second-order frequency is about five times that of the first-order, and the range of the third-order frequency is 15 times or more.
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Oñate, Eugenio. "Slender Plane Beams. Euler-Bernoulli Theory." In Structural Analysis with the Finite Element Method Linear Statics, 1–36. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-1-4020-8743-1_1.
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Carlsson, H., and R. Glowinski. "Vibrations of Euler-Bernoulli Beams with Pointwise Obstacles." In Advances in Kinetic Theory and Continuum Mechanics, 261–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-50235-4_23.
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"Euler Beam Theory." In Encyclopedia of Thermal Stresses, 1336. Dordrecht: Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-007-2739-7_100205.
Full textConference papers on the topic "Euler Beam Theory"
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Kahrobaiyan, M. H., M. Zanaty, and S. Henein. "An Analytical Model for Beam Flexure Modules Based on the Timoshenko Beam Theory." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67512.
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Short beams are the key building blocks in many compliant mechanisms. Hence, deriving a simple yet accurate model of their elastokinematics is an important issue. Since the Euler-Bernoulli beam theory fails to accurately model these beams, we use the Timoshenko beam theory to derive our new analytical framework in order to model the elastokinematics of short beams under axial loads. We provide exact closed-form solutions for the governing equations of a cantilever beam under axial load modeled by the Timoshenko beam theory. We apply the Taylor series expansions to our exact solutions in order to capture the first and second order effects of axial load on stiffness and axial shortening. We show that our model for beam flexures approaches the model based on the Euler-Bernoulli beam theory when the slenderness ratio of the beams increases. We employ our model to derive the stiffness matrix and axial shortening of a beam with an intermediate rigid part, a common element in the compliant mechanisms with localized compliance. We derive the lateral and axial stiffness of a parallelogram flexure mechanism with localized compliance and compare them to those derived by the Euler-Bernoulli beam theory. Our results show that the Euler-Bernoulli beam theory predicts higher stiffness. In addition, we show that decrease in slenderness ratio of beams leads to more deviation from the model based on the Euler-Bernoulli beam theory.
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Ribeiro, Aureliano, José Juliano de Lima Junior, and Felipe Eloy. "DIFFERENTIAL TRANSFORM METHOD APPLIED TO EULER-BERNOULLI BEAM THEORY." In 25th International Congress of Mechanical Engineering. ABCM, 2019. http://dx.doi.org/10.26678/abcm.cobem2019.cob2019-2420.
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Aldraihem, Osama J., Robert C. Wetherhold, and Tarunraj Singh. "A Comparison of the Timoshenko Theory and the Euler-Bernoulli Theory for Control of Laminated Beams." In ASME 1996 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/imece1996-0655.
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Abstract In this paper, the governing equations and boundary conditions of laminated beam smart structures are presented. Sensor and actuator layers are included in the beam so as to facilitate vibration supression. Two mathematical models are presented: the shear-deformable (Timoshenko) model and the shear-indeformable (Euler-Bernoulli) model. The differential equations for a continuous beam are approximated by utilizing finite element techniques for both models. A cantilever laminated beam with and without a tip mass is investigated to assess the validity and the accuracy of the two models when used for vibration supression. Comparison between the two models is presented to show the advantages and the limitations of each of the models. Since the Timoshenko beam theory is higher order than the Euler-Bernoulli theory, it is known to be superior in predicting the transient response of the beam. The superiority of the Timoshenko model is more pronounced for beams with a low aspect ratio. It is shown that use of an Euler-Bernoulli model to represent beam dynamics can lead to the design of an unstable controller.
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Bauchau, Olivier A., and Shilei Han. "Advanced Beam Theory for Multibody Dynamics." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12416.
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In flexible multibody systems, many components are often approximated as beams or shells. More often that not, classical beam theories, such as Euler-Bernoulli beam theory, form the basis of the analytical development for beam dynamics. The advantage of this approach is that it leads to a very simple kinematic representation of the problem: the beam’s section is assumed to remain plane and its displacement field is fully defined by three displacement and three rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from Saint-Venant’s theory for torsion that the cross-section will warp under torque, leading to a three-dimensional deformation state that generates a complex stress state. To overcome this problem, sectional stiffnesses are computed based on sophisticated mechanics of material theories that evaluate the complete state of deformation. These sectional stiffnesses are then used within the framework of an Euler-Bernoulli beam theory based on far simpler kinematic assumptions. While this approach works well for simple cross-sections made of homogeneous material, very inaccurate predictions result for realistic sections, specially for thin-walled beams, or beams made of anisotropic materials. This paper presents a different approach to the problem. Based on a finite element discretization of the cross-section, an exact solution of the theory of three-dimensional elasticity is developed. The only approximation is that inherent to the finite element discretization. The proposed approach is based on the Hamiltonian formalism and leads to an expansion of the solution in terms of extremity and central solutions, as expected from Saint-Venant’s principle.
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Stolte, James, and Joseph M. Santiago. "Determination of Reflection and Transmission Coefficients in Rigidly Connected Beams Using Timoshenko Beam Theory." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/cie-1614.
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Abstract Knowledge of the behavior of a wave incident at a joint is necessary to properly analyze the vibration of a structure. We need to know how much energy is reflected and transmitted and also the type of wave carrying the energy. Typically, Euler beam theory is used to derive the reflection and transmission coefficients at high frequencies. Errors can become unacceptably large in the frequency range currently being analyzed using Statistical Energy Analysis (SEA) and the Power Flow Finite Element Method (PFFEM). We derive reflection and transmission coefficients due to a bending wave incident on a rigid joint between two infinitely long beams using Timoshenko theory and compare results to those obtained using Euler theory. We also compute the reflection and transmission efficiencies that determine the amount of power carried by each wave.
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Zhang, Yichi, and Bingen Yang. "Medium Frequency Vibration Analysis of Beam Structures Modeled by the Timoshenko Beam Theory." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23098.
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Abstract Vibration analysis of complex structures at medium frequencies plays an important role in automotive engineering. Flexible beam structures modeled by the classical Euler-Bernoulli beam theory have been widely used in many engineering problems. A kinematic hypothesis in the Euler-Bernoulli beam theory is that plane sections of a beam normal to its neutral axis remain normal when the beam experiences bending deformation, which neglects the shear deformation of the beam. However, as observed by researchers, the shear deformation of a beam component becomes noticeable in high-frequency vibrations. In this sense, the Timoshenko beam theory, which describes both bending deformation and shear deformation, may be more suitable for medium-frequency vibration analysis of beam structures. This paper presents an analytical method for medium-frequency vibration analysis of beam structures, with components modeled by the Timoshenko beam theory. The proposed method is developed based on the augmented Distributed Transfer Function Method (DTFM), which has been shown to be useful in various vibration problems. The proposed method models a Timoshenko beam structure by a spatial state-space formulation in the s-domain, without any discretization. With the state-space formulation, the frequency response of a beam structure, in any frequency region (from low to very high frequencies), can be obtained in an exact and analytical form. One advantage of the proposed method is that the local information of a beam structure, such as displacements, bending moment and shear force at any location, can be directly obtained from the space-state formulation, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated with the FEA in numerical examples, where the efficiency and accuracy of the proposed method is present. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are illustrated through comparison of the Timoshenko beam theory and the Euler-Bernoulli beam theory.
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Park, S. K., and X. L. Gao. "A New Bernoulli-Euler Beam Model Based on a Modified Couple Stress Theory." In 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments and Second NASA/ARO/ASCE Workshop on Granular Materials in Lunar and Martian Exploration. Reston, VA: American Society of Civil Engineers, 2006. http://dx.doi.org/10.1061/40830(188)166.
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Zhu, Yang, Jean W. Zu, and Minghui Yao. "Modeling of Piezoelectric Energy Harvester: A Comparison Between Euler-Bernoulli Theory and Timoshenko Theory." In ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2011. http://dx.doi.org/10.1115/smasis2011-4995.
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Harvesting vibration energy using piezoelectric materials has gained considerable attention over the past few years. Typically, a piezoelectric energy harvester is a unimorph or bimorph cantilevered beam which undergoes base vibration. The focus of this paper is to compare the Euler-Bernoulli model and the Timoshenko model, which are both used for modeling the vibration-based energy harvester. Procedures of deriving the electro-mechanical equation of motion are provided, following exact expressions for the electrical output in two models. Parametric case studies are carried out in order to compare the frequency response of two models. Simulation results show that there is a great difference between Euler-Bernoulli model and Timoshenko model at low length-to-thickness aspect ratio. Such difference diminishes and becomes negligible as aspect ratio increases. It is shown that for the design of piezoelectric energy harvester with small aspect ratio, Timoshenko model can be more accurate than Euler-Bernoulli model in predicting the system behavior.
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Wang, Lin, and Yan Wang. "Study on Coupling Between Euler Beam and Nonlinear Solitary Wave Based on Cosserat Theory." In 2020 15th Symposium on Piezoelectrcity, Acoustic Waves and Device Applications (SPAWDA). IEEE, 2021. http://dx.doi.org/10.1109/spawda51471.2021.9445420.
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De Rosa, Maria Anna, Maria Lippiello, Hector Martin, and Francesco Vairo. "Free vibration analysis of embedded SWCNTs using DQM based on nonlocal Euler-Bernoulli beam theory." In 2013 International Conference on Advanced Computer Science and Electronics Information. Paris, France: Atlantis Press, 2013. http://dx.doi.org/10.2991/icacsei.2013.52.
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