Relevant bibliographies by topics / Timoshenko beam theory

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Timoshenko beam theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 September 2023

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Journal articles on the topic "Timoshenko beam theory"

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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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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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Park, Young-Ho, and Suk-Yoon Hong. "Vibrational Energy Flow Analysis of Corrected Flexural Waves in Timoshenko Beam – Part I: Theory of an Energetic Model." Shock and Vibration 13, no. 3 (2006): 137–65. http://dx.doi.org/10.1155/2006/308715.

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In this paper, an energy flow model is developed to analyze transverse vibration including the effects of rotatory inertia as well as shear distortion, which are very important in the Timoshenko beam transversely vibrating in the medium-to-high frequency ranges. The energy governing equations for this energy flow model are newly derived by using classical displacement solutions of the flexural motion for the Timoshenko beam, in detail. The derived energy governing equations are in the general form incorporating not only the Euler-Bernoulli beam theory used for the conventional energy flow model but also the Rayleigh, shear, and Timoshenko beam theories. Finally, to verify the validity and accuracy of the derived model, numerical analyses for simple finite Timoshenko beams were performed. The results obtained by the derived energy flow model for simple finite Timoshenko beams are compared with those of the classical solutions for the Timoshenko beam, the energy flow solution, and the classical solution for the Euler-Bernoulli beam with various excitation frequencies and damping loss factors of the beam. In addition, the vibrational energy flow analyses of coupled Timoshenko beams are described in the other companion paper.
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Wan, Chunfeng, Huachen Jiang, Liyu Xie, Caiqian Yang, Youliang Ding, Hesheng Tang, and Songtao Xue. "Natural Frequency Characteristics of the Beam with Different Cross Sections Considering the Shear Deformation Induced Rotary Inertia." Applied Sciences 10, no. 15 (July 29, 2020): 5245. http://dx.doi.org/10.3390/app10155245.

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Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.
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Hilton, Harry H. "Viscoelastic Timoshenko beam theory." Mechanics of Time-Dependent Materials 13, no. 1 (December 2, 2008): 1–10. http://dx.doi.org/10.1007/s11043-008-9075-4.

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Shi, Guangyu, and Qiaorong Guo. "On the Appropriate Rotary Inertia in Timoshenko Beam Theory." International Journal of Applied Mechanics 13, no. 04 (May 2021): 2150055. http://dx.doi.org/10.1142/s1758825121500551.

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The rotary inertia defined by Timoshenko to account for the angular velocity effect in flexural vibration of beams has been questioned by some researchers in recent years, and it caused some confusions. This paper discusses the appropriate rotary inertia in Timoshenko beam theory (TBT) and evaluates the influence of the two forms of the rotary inertia on the prediction of the higher-mode frequencies of transversely vibrating beams. Based on the theory of elasticity and variational principle, this work shows that the rotary inertia in the original TBT, defined in terms of the rotation of beam cross-section induced by bending deformation, is variational consistent and is capable of yielding good results of the phase velocities of transversely vibrating beams even in the case where the wavelength of vibrating beams approaches the beam height. On the other hand, the so-called corrected TBT, in which the rotary inertia is defined in terms of the slope of beam deflection, is neither variational consistent nor accurate when the wavelength of vibrating beams approaches the beam height. Therefore, the rotary inertia in TBT defined by Timoshenko is correct and should be used in the dynamic analysis of beams.
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Cao, MS, W. Xu, Z. Su, W. Ostachowicz, and N. Xia. "Local coordinate systems-based method to analyze high-order modes of n-step Timoshenko beam." Journal of Vibration and Control 23, no. 1 (August 9, 2016): 89–102. http://dx.doi.org/10.1177/1077546315573919.

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High-frequency transverse vibration of stepped beams has attracted increasing attention in various industrial areas. For an n-step Timoshenko beam, the governing differential equations of transverse vibration have been well established in the literature on the basis of assembling classic Timoshenko beam equations for uniform beam segments. However, solving the governing differential equation has not been resolved well to date, manifested by a computational bottleneck: only the first k modes ( k ≤ 12) are solvable for i-step ( i ≥ 0) Timoshenko beams. This bottleneck diminishes the completeness of stepped Timoshenko beam theory. To address this problem, this study first reveals the root cause of the bottleneck in solving the governing differential equations for high-order modes, and then creates a sophisticated method, based on local coordinate systems, that can overcome the bottleneck to accomplish high-order mode shapes of an n-step Timoshenko beam. The proposed method uses a set of local coordinate systems in place of the conventional global coordinate system to characterize the transverse vibration of an n-step Timoshenko beam. With the method, the local coordinate systems can simplify the frequency equation for the vibration of an n-step Timoshenko beam, making it possible to obtain high-order modes of the beam. The accuracy, capacity, and efficiency of the method based on local coordinate systems in acquiring high-order modes are corroborated using the well-known exact dynamic stiffness method underpinned by the Wittrick-Williams algorithm as a reference. Removal of the bottlenecks in solving the governing differential equations for high-order modes contributes usefully to the completeness of stepped Timoshenko beam theory.
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Hutchinson, J. R. "Shear Coefficients for Timoshenko Beam Theory." Journal of Applied Mechanics 68, no. 1 (August 15, 2000): 87–92. http://dx.doi.org/10.1115/1.1349417.

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The Timoshenko beam theory includes the effects of shear deformation and rotary inertia on the vibrations of slender beams. The theory contains a shear coefficient which has been the subject of much previous research. In this paper a new formula for the shear coefficient is derived. For a circular cross section, the resulting shear coefficient that is derived is in full agreement with the value most authors have considered “best.” Shear coefficients for a number of different cross sections are found.
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Hutchinson, J. R., and S. D. Zillmer. "On the Transverse Vibration of Beams of Rectangular Cross-Section." Journal of Applied Mechanics 53, no. 1 (March 1, 1986): 39–44. http://dx.doi.org/10.1115/1.3171735.

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An exact solution for the natural frequencies of transverse vibration of free beams with rectangular cross-section is used as a basis of comparison for the Timoshenko beam theory and a plane stress approximation which is developed herein. The comparisons clearly show the range of applicability of the approximate solutions as well as their accuracy. The choice of a best shear coefficient for use in the Timoshenko beam theory is considered by evaluation of the shear coefficient that would make the Timoshenko beam theory match the exact solution and the plane stress solution. The plane stress solution is shown to provide excellent accuracy within its range of applicability.
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Ghayesh, Mergen H., Ali Farajpour, and Hamed Farokhi. "Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams." Vibration 2, no. 2 (June 14, 2019): 201–21. http://dx.doi.org/10.3390/vibration2020013.

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A nonlinear vibration analysis is conducted on the mechanical behavior of axially functionally graded (AFG) microscale Timoshenko nonuniform beams. Asymmetry is due to both the nonuniform material mixture and geometric nonuniformity. Using the Timoshenko beam theory, the continuous models for translation/rotation are developed via an energy balance. Size-dependence is incorporated via the modified couple stress theory and the rotation via the Timoshenko beam theory. Galerkin’s method of discretization is applied and numerical simulations are conducted for a size-dependent vibration of the AFG microscale beam. Effects of material gradient index and axial change in the cross-sectional area on the force and frequency diagrams are investigated.
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Dissertations / Theses on the topic "Timoshenko 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 discussed
these 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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O'Leary, Beth Andrews. "Analysis of high-speed rotating systems using Timoshenko beam theory in conjunction with the transfer matrix method /." Online version of thesis, 1989. http://hdl.handle.net/1850/10608.

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Hayes, Michael David. "Structural Analysis of a Pultruded Composite Beam: Shear Stiffness Determination and Strength and Fatigue Life Predictions." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/11066.

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This dissertation is focused on understanding the performance of a particular fiber-reinforced polymeric composite structural beam, a 91.4 cm (36 inch) deep pultruded double-web beam (DWB) designed for bridge construction. Part 1 focuses on calculating the Timoshenko shear stiffness of the DWB and understanding what factors may introduce error in the experimental measurement of the quantity for this and other sections. Laminated beam theory and finite element analysis (FEA) were used to estimate the shear stiffness. Several references in the literature have hypothesized an increase in the effective measured shear stiffness due to warping. A third order laminated beam theory (TLBT) was derived to explore this concept, and the warping effect was found to be negligible. Furthermore, FEA results actually indicate a decrease in the effective shear stiffness at shorter spans for simple boundary conditions. This effect was attributed to transverse compression at the load points and supports. The higher order sandwich theory of Frostig shows promise for estimating the compression related error in the shear stiffness for thin-walled beams. Part 2 attempts to identify the failure mechanism(s) under quasi-static loading and to develop a strength prediction for the DWB. FEA was utilized to investigate two possible failure modes in the top flange: compression failure of the carbon fiber plies and delamination at the free edges or taper regions. The onset of delamination was predicted using a strength-based approach, and the stress analysis was accomplished using a successive sub-modeling approach in ANSYS. The results of the delamination analyses were inconclusive, but the predicted strengths based on the compression failure mode show excellent agreement with the experimental data. A fatigue life prediction, assuming compression failure, was also developed using the remaining strength and critical element concepts of Reifsnider et al. One DWB fatigued at about 30% of the ultimate capacity showed no signs of damage after 4.9 million cycles, although the predicted number of cycles to failure was 4.4 million. A test on a second beam at about 60% of the ultimate capacity was incomplete at the time of publication. Thus, the success of the fatigue life prediction was not confirmed.
Ph. D.
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Balarezo, Salgado José Illarick, and Arroyo Edgard Cristian Corilla. "Análisis de vibración libre de vigas laminadas de materiales compuestos utilizando el método de elementos finitos." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2021. http://hdl.handle.net/10757/657266.

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Se presenta un modelo de elementos finitos que describe el comportamiento de vibración de libre de vigas compuestas laminadas. Se desarrolla el modelo utilizando el principio de Hamilton y la teoría de vigas Timoshenko que incluye deformaciones por corte. Se asume interpolaciones de alto orden para la aproximación de las variables fundamentales. Los laminados compuestos son ortotrópicos con fibras orientadas en diferentes direcciones. Se implementa un programa para materiales compuestos laminado en MATLAB. Se comparan resultados con otros obtenidos en la literatura para validar el modelo. Se realiza un estudio de convergencia y paramétrico con un mismo número de lámina y diferentes direcciones. Se verifica que la formulación que es bastante precisa con resultados satisfactorios en la investigación.
In this work, is presented a finite element model that describes the free vibration behavior of laminated composite beams. The model is developed by the Hamilton principle and the Timoshenko theory that includes shear deformations. Composite laminates are assumed to be orthotropic with fibers oriented in different directions, such as Angle Ply and Cross Ply cases. This investigation works out on a MAPLE program for laminated composites materials that will be completed all in MATLAB program. In order to validate the model, the results are compared with different literatures, also verify the formulation that is quite accurate and obtain quite satisfactory results in the investigation. High order interpolations are assumed to approximate fundamental variables. A convergence study and parametric study will be carried out with the same number of laminas in different directions.
Tesis
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Martins, Jaime Florencio. "Influência da inércia de rotação e da força cortante nas freqüências naturais e na resposta dinâmica de estruturas de barras." Universidade de São Paulo, 1998. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-18042018-102329/.

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A clássica teoria de Euler-Bernoulli para vibrações transversais de vigas elásticas é sabido não ser adequada para vibrações de altas freqüências, como é o caso de vibração de vigas curtas. Esta teoria assume que a deflexão deve-se somente ao momento fletor, uma vez que os efeitos da inércia de rotação e da força cortante são negligenciados. Lord Rayleigh complementou a teoria clássica demonstrando a contribuição da inércia de rotação e Timoshenko estendeu a teoria ao incluir os efeitos da força cortante. A equação resultante é conhecida como sendo a que caracteriza a chamada teoria de viga de Timoshenko. Usando-se a matriz de rigidez dinâmica, as freqüências naturais e a resposta dinâmica de estruturas de barras são determinadas e comparadas de acordo com resultados de quatro modelos de vibração. São estudados o problema de vibração flexional de vigas, pórticos e grelhas, bem como o problema de fundação elástica segundo o modelo de Winkler e também a versão mais avançada que é o modelo de Pasternak.
Classical Euler-Bernoulli theory for transverse vibrations of elastic beams is known to be inadequate to consider high frequency modes which occur for short beams, for example. This theory is derived under the assumption that the deflection is only due to bending. The effects of rotary inertia and shear deformation are ignored. Lord Rayleigh improved the classical theory by considering the effect of rotary inertia. Timoshenko extended the theory to include the effects of shear deformation. The resulting equation is known as Timoshenko beam theory. The natural frequencies and dynamic reponse of framed structures are determined by using the dynamic stiffness matrix and compered according to these theories. The flexional vibration problems of beams, plane frames and grids are analysed, as well problems of elastic foundation according the well known Winkler model and also the more general Pasternak model.
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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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Dlugoš, Jozef. "Výpočtové modelování dynamiky pístního kroužku." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2014. http://www.nusl.cz/ntk/nusl-231299.

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Piston rings are installed in the piston and cylinder wall, which does not have a perfect round shape due to machining tolerances or external loads e.g. head bolts tightening. If the ring cannot follow these deformations, a localized lack of contact will occur and consequently an increase in the engine blow-by and lubricant oil consumption. Current 2D computational methods can not implement such effects – more complex model is necessary. The presented master’s thesis is focused on the developement of a flexible 3D piston ring model able to capture local deformations. It is based on the Timoshenko beam theory in cooperation with MBS software Adams. Model is then compared with FEM using software ANSYS. The validated piston ring model is assembled into the piston/cylinder liner and very basic simulations are run. Finally, future improvements are suggested.
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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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Balarezo, Salgado José Illarick, and Arroyo Edgard Cristian Corilla. "Análisis de vibración libre de vigas laminadas de materiales compuestos utilizando el método de elementos finitos." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2001. http://hdl.handle.net/10757/654828.

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Esta investigación se enfoca en el análisis de vibración libre de vigas Timoshenko utilizando el método de elementos finitos. Se desarrolla el modelo utilizando el principio de Hamilton y la teoría de vigas Timoshenko que incluye deformaciones por corte. Se asume interpolaciones de alto orden para la aproximación de las variables fundamentales. Los materiales para emplear son isotrópicos. Se implementa un programa para estos materiales en MATLAB. Se comparan resultados con otros obtenidos en la literatura para validar el modelo. Se realiza un estudio paramétrico con una misma longitud y diferentes esbelteces. Se verifica que la formulación sea bastante precisa con resultados muy satisfactorios.
This research focuses on the free vibration analysis of Timoshkenko beams using the finite element method. The model is developed using the Hamilton principle and the Timoshenko beam theory that includes shear deformations. high order interpolations are assumed for the approximation of the fundamental variables. The materials to be used are isotropic. A program for these materials is implemented in MATLAB. Results are compared with others obtained in the literature to validate the model. A parametric study is carried out with the same length and different slenderness. It is verified that the formulation is quite precise with satisfactory results to the investigation.
Trabajo de investigación
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Balarezo, Salgado José Illarick, and Arroyo Edgard Cristian Corilla. "Vibración libre de vigas de material isotrópico utilizando el método de elementos finitos." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2021. http://hdl.handle.net/10757/654828.

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Esta investigación se enfoca en el análisis de vibración libre de vigas Timoshenko utilizando el método de elementos finitos. Se desarrolla el modelo utilizando el principio de Hamilton y la teoría de vigas Timoshenko que incluye deformaciones por corte. Se asume interpolaciones de alto orden para la aproximación de las variables fundamentales. Los materiales para emplear son isotrópicos. Se implementa un programa para estos materiales en MATLAB. Se comparan resultados con otros obtenidos en la literatura para validar el modelo. Se realiza un estudio paramétrico con una misma longitud y diferentes esbelteces. Se verifica que la formulación sea bastante precisa con resultados muy satisfactorios.
This research focuses on the free vibration analysis of Timoshkenko beams using the finite element method. The model is developed using the Hamilton principle and the Timoshenko beam theory that includes shear deformations. high order interpolations are assumed for the approximation of the fundamental variables. The materials to be used are isotropic. A program for these materials is implemented in MATLAB. Results are compared with others obtained in the literature to validate the model. A parametric study is carried out with the same length and different slenderness. It is verified that the formulation is quite precise with satisfactory results to the investigation.
Trabajo de investigación
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Books on the topic "Timoshenko beam theory"

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Haque, Aamer. Timoshenko Beam Theory. Independently Published, 2018.

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Haque, Aamer. Timoshenko Beam Theory. Independently Published, 2019.

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Book chapters on the topic "Timoshenko beam theory"

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Öchsner, Andreas. "Timoshenko Beam Theory." In Classical Beam Theories of Structural Mechanics, 67–104. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76035-9_3.

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Chen, D., and L. Zhang. "Harmonic Vibration of Inclined Porous Nanocomposite Beams." In Lecture Notes in Civil Engineering, 497–501. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-3330-3_52.

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AbstractThis work investigated the linear harmonic vibration responses of inclined beams featured by closed-cell porous geometries where the bulk matrix materials were reinforced by graphene platelets as nanofillers. Graded and uniform porosity distributions combined with different nanofiller dispersion patterns were applied in the establishment of the constitutive relations, in order to identify their effects on beam behavior under various harmonic loading conditions. The inclined beam model comprised of multiple layers and its displacement field was constructed using Timoshenko theory. Forced vibration analysis was conducted to predict the time histories of mid-span deflections, considering varying geometrical and material characterizations. The findings may provide insights into the development of advanced inclined nanocomposite structural components under periodic excitations.
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Rao, Priya, S. Chakraverty, and Debanik Roy. "Dynamics of Slender Single-Link Flexible Robotic Manipulator Based on Timoshenko Beam Theory." In Mathematical Methods in Dynamical Systems, 273–90. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9781003328032-10.

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Kondo, Kyohei. "Analysis of Potential Energy Release Rate of Composite Laminate Based on Timoshenko Beam Theory." In Advances in Composite Materials and Structures, 513–16. Stafa: Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-427-8.513.

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Amouzadrad, P., S. C. Mohapatra, and C. Guedes Soares. "Hydroelastic response of a moored floating flexible structure based on Timoshenko-Mindlin beam theory." In Advances in the Analysis and Design of Marine Structures, 265–73. London: CRC Press, 2023. http://dx.doi.org/10.1201/9781003399759-29.

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Amouzadrad, P., S. C. Mohapatra, and C. Guedes Soares. "Hydroelastic response of a moored floating flexible offshore structure based on Timoshenko-Mindlin-Beam theory." In Trends in Renewable Energies Offshore, 879–87. London: CRC Press, 2022. http://dx.doi.org/10.1201/9781003360773-97.

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Zhang, Yunpeng, and Bo Diao. "Comparison of Nonlinear Analysis of RC Cross-Section Based on Timoshenko with Higher-Order Shear Deformation Beam Theory." In Recent Advances in Computer Science and Information Engineering, 223–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25766-7_29.

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Oñate, Eugenio. "Thick/Slender Plane Beams. Timoshenko Theory." In Structural Analysis with the Finite Element Method Linear Statics, 37–97. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-1-4020-8743-1_2.

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"The Timoshenko Beam Theory and Its Extension." In Symplectic Elasticity, 63–95. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812778727_0003.

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"Intermediate Theory Between the Bernoulli–Euler and the Timoshenko–Ehrenfest Beam Theories: Truncated Timoshenko–Ehrenfest Equations." In Handbook on Timoshenko-Ehrenfest Beam and Uflyand-Mindlin Plate Theories, 139–83. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813236523_0003.

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Conference papers on the topic "Timoshenko beam theory"

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Banerjee, J. Ranjan, David Kennedy, and Isaac Elishakoff. "Further Insights Into the Timoshenko-Ehrenfest Beam Theory." In ASME 2022 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/imece2022-96554.

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Abstract In this paper, the theory of a Timoshenko-Ehrenfest beam is revisited and given a new perspective with particular emphasis on the relative significances of the parameters underlying the theory. The investigation is intended to broaden the scope and applicability of the theory. It has been shown that the two parameters that characterise the Timoshenko-Ehrenfest beam theory, namely the rotary inertia and the shear deformation, can be related and hence they can be combined into one parameter when predicting the beam’s free vibration behaviour. A theoretical proof is given that explains why the effect of the shear deformation on the free vibration behaviour of a Timoshenko-Ehrenfest beam for any boundary condition will be always more pronounced than that of the rotary inertia. The range of applicability of the Timoshenko-Ehrenfest beam theory for realistic problems is demonstrated by a set of new curves, which provide considerable insights into the 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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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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Zirkelback, Nicole L., and Jerry H. Ginsberg. "Ritz Series Analysis of Rotating Machinery Incorporating Timoshenko Beam Theory." In ASME Turbo Expo 2001: Power for Land, Sea, and Air. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/2001-gt-0244.

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A shaft with attached rigid disks is modeled as a rotating Timoshenko beam supported by general compliant, nonconservative bearing supports. The continuous shaft-disk system is described with kinetic and potential energy functionals that fully account for transverse shear, translational and rotatory inertia, and gyroscopic coupling. Ritz series expansions are used to describe the flexural displacements and cross-sectional rotations about orthogonal fixed axes. The equations of motion are derived from Lagrange’s equations and placed in a state-space form that preserves the skew-symmetric gyroscopic matrix, as well as the cross-coupling displacement and velocity coefficient matrices describing the effects of bearings. Both the general and adjoint eigenproblems for the nonsymmetric equations are solved. Bi-orthogonality conditions lead to the ability to evaluate dynamic response via modal analysis. Two examples, which show close agreement with prior analyses of critical speeds, demonstrate the ease with which the method may be applied.
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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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Chiu, Rong, and Wenbin Yu. "Heterogeneous Beam Element Based on Timoshenko Beam Model." In ASME 2022 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/imece2022-94187.

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Abstract Traditional multiscale methods homogenize a beam-like structure into a material point in 1-D continuum with effective properties computed over a structure gene in terms of a cross-section or a 3D segment with spanwise periodicity. Such methods lose accuracy when dealing with real world beam-like structures usually not uniform or periodic along the spanwise direction. Thus, traditional multiscale methods cannot be rigorously applied to these cases. In our previous work, a new multiscale method was proposed based on a novel application of the recently developed Mechanics of Structure Genome (MSG) to analyze beam-like structures. Beam-like structures were homogenized into a series of 3-node Heterogeneous Beam Elements (HBE) with 18 × 18 effective beam element stiffness matrices, which were used as input for one-dimensional beam analyses. However, due to the shape function limitations, HBE could not handle transverse shear loads. In this work, the shape functions and the MSG theory are further modified to enable capabilities of HBE for transverse shear loads. Using the macroscopic behavior of the beam elements as input, dehomogenization can be performed to predict the local stresses and strains in the original structure. Two examples are used (a periodic composite beam and a tapered beam) to demonstrate the capability of this improved HBE.
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Yu, Wenbin, and Dewey Hodges. "The Timoshenko-like Theory of the Variational Asymptotic Beam Sectional Analysis." In 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-1419.

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Chen, X., F. Chen, X. Wang, W. Shen, and H. Yu. "An improved bond-based peridynamic model based on Timoshenko beam theory." In 14th WCCM-ECCOMAS Congress. CIMNE, 2021. http://dx.doi.org/10.23967/wccm-eccomas.2020.063.

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Xie, M., F. M. L. Amirouche, and M. Valco. "Dynamic Analysis of Gear Meshing Teeth Using Modified Timoshenko Beam Theory." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0057.

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Abstract An explicit dynamical formulation of the gear meshing teeth using modified Timoshenko beam theory is presented in this paper. The acting position direction and magnitude of the external force is assumed time variant. The meshing tooth is modeled as a cantilever beam where the inertia forces due to the large rotation of the tooth base, as well as the external equivalent axial force and moment are all included in the equations of motion. Computer algorithms for gear dynamics based on the theory developed is presented. In the numerical simulations, the involute for the gear tooth profile is considered.
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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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Reports on the topic "Timoshenko beam theory"

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Tang, Yi-Qun, and Yao-Peng Liu. SECOND-ORDER ELASITC ANALYSIS OF TWO-DIMENSIONAL FRAMES BASED ON TIMOSHENKO BEAM THEORY. The Hong Kong Institute of Steel Construction, December 2018. http://dx.doi.org/10.18057/icass2018.p.161.

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