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Journal articles on the topic 'Timoshenko equivalent beam'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Ferretti, Manuel, and Francesco D’Annibale. "Buckling of Planar Micro-Structured Beams." Applied Sciences 10, no. 18 (2020): 6506. http://dx.doi.org/10.3390/app10186506.

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In this paper, a Timoshenko beam model is formulated for buckling analysis of periodic micro-structured beams, uniformly compressed. These are planar grid beams, whose micro-structure consists of a square lattice of equal fibers, modeled as Timoshenko micro-beams. The equivalent beam model is derived in the framework of a direct one-dimensional approach and its constitutive law, including the effect of prestress of the longitudinal fibers, is deduced through a homogenization approach. Accordingly, micro–macro constitutive relations are obtained through an energy equivalence between a cell of t

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2

D’Annibale, Francesco, Manuel Ferretti, and Angelo Luongo. "Static and Dynamic Responses of Micro-Structured Beams." Applied Sciences 10, no. 19 (2020): 6836. http://dx.doi.org/10.3390/app10196836.

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In this study, we developed a one-dimensional Timoshenko beam model, embedded in a 3D space for static and dynamic analyses of beam-like structures. These are grid cylinders, that is, micro-structured bodies, made of a periodic and specifically designed three-dimensional assembly of beams. Derivation is performed in the framework of the direct 1D approach, while the constitutive law is determined by a homogenization procedure based on an energy equivalence between a cell of the periodic model and a segment of the solid beam. Warping of the cross-section, caused by shear and torsion, is approxi

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3

Fu, Chao. "Vibration Analysis of Viscoelastic Timoshenko Cracked Beams with Massless Viscoelastic Rotational Spring Models." Journal of Applied Mathematics 2023 (July 31, 2023): 1–11. http://dx.doi.org/10.1155/2023/2341137.

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Based on the equivalent bending stiffness of the viscoelastic cracked beam with open cracks, the corresponding complex frequency characteristic equations of a Timoshenko viscoelastic cracked beam are obtained by using the method of separation of variables and the Laplace transform. The vibration characteristics of a viscoelastic Timoshenko cracked beams with the standard linear solid model and Kelvin-Voigt model are investigated. By numerical examples, the effects of the crack location, crack number, crack depth, and slenderness ratio on the vibration characteristics of the viscoelastic cracke

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4

Cluni, Federico, Stefano Fiorucci, Vittorio Gusella, and Massimiliano Gioffrè. "Estimation of the Mechanical Parameters for a Reduced Coupled Flexural–Torsional Beam Model of a Tall Building by a Sub-Structure Approach." Applied Sciences 11, no. 10 (2021): 4655. http://dx.doi.org/10.3390/app11104655.

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The use of equivalent beam models to estimate the dynamical characteristics of complex tall buildings has been investigated by several authors. The main reason is the structural response estimation to stochastic loads, such as wind and earthquake, using a reduced number of degrees of freedom, which reduces the computational costs and therefore gives the designer an effective tool to explore a number of possible structural solutions. In this paper, a novel approach to calibrate the mechanical and dynamical features of a complete 3D Timoshenko beam, i.e., describing bending, shear and torsional

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5

Xing, Yufeng, Lingyu Meng, Zhiwei Huang, and Yahe Gao. "A Novel Efficient Prediction Method for Microscopic Stresses of Periodic Beam-like Structures." Aerospace 9, no. 10 (2022): 553. http://dx.doi.org/10.3390/aerospace9100553.

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This paper presents a novel superposition method for effectively predicting the microscopic stresses of heterogeneous periodic beam-like structures. The efficiency is attributed to using the microscopic stresses of the unit cell problem under six generalized strain states to construct the structural microscopic stresses. The six generalized strain states include one unit tension strain, two unit bending strains, one unit torsion strain, and two linear curvature strains of a Timoshenko beam. The six microscopic stress solutions of the unit cell problem under these six strain states have previou

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6

Zhang, Yi, Li Chen, Guo Liang Cheng, and Qing Hua Li. "Non-Dimensional Vibration of Timoshenko Beams with Axial Loads." Advanced Materials Research 368-373 (October 2011): 1577–82. http://dx.doi.org/10.4028/www.scientific.net/amr.368-373.1577.

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The paper is supposed to establish a non-dimensional approach to analyze the free vibration of axially loaded beams with different kinds of boundary conditions, based on the Timoshenko’s beam theory and the method of separation of variables. When the mode-shapes and frequencies are known, it is convenient to get the equivalent load vector, equivalent mass matrix and the frequencies matrix, then, the characteristics of vibration of axially loaded beams will be obtained by the approach. The results and conclusions were also helpful to the anti-blast analysis of columns

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7

Khiem, Nguyen Tien, and Duong The Hung. "A closed-form solution for free vibration of multiple cracked Timoshenko beam and application." Vietnam Journal of Mechanics 39, no. 4 (2017): 315–28. http://dx.doi.org/10.15625/0866-7136/9641.

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A closed-form solution for free vibration is constructed and used for obtaining explicit frequency equation and mode shapes of Timoshenko beams with arbitrary number of cracks. The cracks are represented by the rotational springs of stiffness calculated from the crack depth. Using the obtained frequency equation, the sensitivity of natural frequencies to crack of the beams is examined in comparison with the Euler-Bernoulli beams. Numerical results demonstrate that the Timoshenko beam theory is efficiently applicable not only for short or fat beams but also for the long or slender ones. Neverth

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8

Li, Xiao, Shi Ping Li, Xu Dong Shi, and Min Ding. "Interpolation-Element for Beam on Winkler Elastic Foundation." Applied Mechanics and Materials 467 (December 2013): 354–60. http://dx.doi.org/10.4028/www.scientific.net/amm.467.354.

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On the basis of the deformation characteristics of Euler and Timoshenko beams on Winkler elastic foundation, the displacement shape functions were created. Lagrange interpolation function was used for the deformation in the axial direction, and Hermite interpolation function was applied in the bending direction. By applying the principle of minimum potential energy, energy integral and variation, the stiffness matrixes and equivalent load arrays of Euler and Timoshenko beams were derived. The model of elastic foundation beam was built by using elements constructed in this paper. And the beam d

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9

White, M. W. D., and G. R. Heppler. "Vibration of a Rotating Timoshenko Beam." Journal of Vibration and Acoustics 118, no. 4 (1996): 606–13. http://dx.doi.org/10.1115/1.2888341.

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Timoshenko beam theory is used to model a flexible slewing link with an attached payload using two different rotating frames of reference: pseudo-pinned and pseudo-clamped. The boundary conditions are presented for both formulations; these lead naturally to the frequency equation for the link. The infinite dimensional model of the slewing link is then approximated by a finite dimensional model. Finally, these two formulations are shown to be equivalent through a simple transformation.

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10

Liu, Xuemei, and Zichen Deng. "Generalized Multi-Symplectic Numerical Implementation of Dynamic Responses for Saturated Poroelastic Timoshenko Beam." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 38, no. 4 (2020): 774–83. http://dx.doi.org/10.1051/jnwpu/20203840774.

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Based on the porous media theory and Timoshenko beam theory, properties of dynamic responses in fluid-solid coupled incompressible saturated poroelastic Timoshenko beam are investigated by generalized multi-symplectic method. Dynamic response equation set of incompressible saturated poroelastic Timoshenko beam is presented at first. Then a first order generalized multi-symplectic form of this dynamic response equation set is constructed, and errors of generalized multi-symplectic conservation law, generalized multi-symplectic local momentum and generalized multi-symplectic local energy are als

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11

Lee, Usik. "Dynamic Characterization of the Joints in a Beam Structure by Using Spectral Element Method." Shock and Vibration 8, no. 6 (2001): 357–66. http://dx.doi.org/10.1155/2001/254020.

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A frequency-domain approach is introduced to identify the dynamic characteristics of the mechanical joints within a one-dimensional structure. In this paper, a cantilevered beam structure with a bolt-joint is considered as an illustrative problem. The beam structure consists of two Timoshenko-beams connected to each other by a bolted joint. The bolt-joint is represented by the equivalent joint model with four parameters, and the four parameters are determined from the experimentally measured frequency response functions (FRF). To improve the accuracy of the identified bolt-joint parameters, th

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12

Guéguen, Philippe, E. Diego Mercerat, and Felipe Alarcon. "Parametric Study on the Interpretation of Wave Velocity Obtained by Seismic Interferometry in Beam‐Like Buildings." Bulletin of the Seismological Society of America 109, no. 5 (2019): 1829–42. http://dx.doi.org/10.1785/0120190054.

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Abstract In this article, we propose an interpretation of the propagation velocities of the pulse wave obtained in vertical structures through seismic interferometry by deconvolution. The novelty of this article is to propose a parametric study applied to canonical finite‐element models of fixed‐base buildings from pure‐shear to pure‐bending beam‐like buildings, adjusted to equivalent Timoshenko beam‐like structures. For given input seismic motions, the time histories of the horizontal displacement at each floor are obtained and used to estimate the propagation velocity of the pulse wave by de

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13

Chen, Wei-Ren, and Heng Chang. "Vibration Analysis of Functionally Graded Timoshenko Beams." International Journal of Structural Stability and Dynamics 18, no. 01 (2018): 1850007. http://dx.doi.org/10.1142/s0219455418500074.

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The vibration behavior of a functionally graded Timoshenko beam is investigated by applying the transformed-section method. The material properties of a functionally graded (FG) beam are assumed to vary across the thickness according to a simple power law. The cross section of FG beam with two constituents is first transformed into an equivalent cross section of the material on the top. Then, the lateral and longitudinal vibration equations of a homogeneous Timoshenko beam are separately applied to the beam with the transformed section. The bending natural frequencies of FG beam are evaluated

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14

Fu, Chao, and Xiao Yang. "Bending of a Viscoelastic Timoshenko Cracked Beam Based on Equivalent Viscoelastic Spring Models." Advances in Civil Engineering 2021 (October 21, 2021): 1–16. http://dx.doi.org/10.1155/2021/8663213.

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Considering the transverse crack as a massless viscoelastic rotational spring, the equivalent stiffness of the viscoelastic cracked beam is derived by Laplace transform and the generalized Dirac delta function. Using the standard linear solid constitutive equation and the inverse Laplace transform, the analytical expressions of the deflection and rotation angle of the viscoelastic Timoshenko beam with an arbitrary number of open cracks are obtained in the time domain. By numerical examples, the bending results of the analytical expressions are verified with those of the FEM program. Additional

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15

Hamidi, Ahmed, Mohamed Zidour, Khaled Bouakkaz, and Tayeb Bensattalah. "Thermal and Small-Scale Effects on Vibration of Embedded Armchair Single-Walled Carbon Nanotubes." Journal of Nano Research 51 (February 2018): 24–38. http://dx.doi.org/10.4028/www.scientific.net/jnanor.51.24.

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The non-local Timoshenko beam theory has been implemented to investigate the free vibration of armchair single-walled carbon nanotubes embedded in elastic medium including the thermal effects. The mechanical properties of nano-composite (carbon nanotubes and polymer matrix) are treated as functions of temperature change and the analytical solution is derived according to the governing equations of non-local Timoshenko beam models. The equivalent Young’s modulus and shear modulus for armchair single-walled carbon nanotubes are derived using an energy-equivalent model. Inﬂuence of small-scale co

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16

Song, Wenchao, Zhongguo John Ma, and Hyoseon Ji. "Equivalent Strip Width for FRP Superstructure Design Using Timoshenko Beam Approximation." Journal of Composites for Construction 17, no. 5 (2013): 744–52. http://dx.doi.org/10.1061/(asce)cc.1943-5614.0000379.

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17

Sabzehzar, Saman, Noorollah Majidi, Ali Shafizadeh, and Hossein Tajmir Riahi. "Proposing a practical equivalent Timoshenko beam for analysis of truss structures." Structures 63 (May 2024): 106401. http://dx.doi.org/10.1016/j.istruc.2024.106401.

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18

Li, Bo, Yan Wang, Yipeng Liu, Jianguo Tao, Hui Ren, and Hui Yang. "Equivalent Continuum Modeling for Flexible Slender Quadrilateral Truss Structure." Machines 12, no. 2 (2024): 111. http://dx.doi.org/10.3390/machines12020111.

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A space in-orbit service simulation experiment platform is a type of equipment platform that allows spacecraft such as satellites and deep-space explorers to be adequately ground tested before launch. The function of the crane system is to drive the target spacecraft to perform a large-scale movement. This study focuses on the dynamics of a space in-orbit service simulation experiment platform with suspension rope and column quadrilateral truss structure as connecting devices. A space in-orbit service simulation experiment platform with a column quadrilateral truss structure as a connecting de

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19

Oyelade, A. O., and O. M. Sadiq. "ENHANCED DAMPING CHARACTERISTICS OF TIMOSHENKO BEAM ON ELASTIC AND METAMATERIAL FOUNDATIONS." Journal of the Serbian Society for Computational Mechanics 14, no. 1 (2020): 52–62. http://dx.doi.org/10.24874/jsscm.2020.14.01.05.

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An analytical model is developed for the flexural wave propagation of a continuous Timoshenko beam resting on elastic and metamaterial foundations. The metamaterial foundation consists of positive and negative springs with a damper. This added negative stiffness component is constructed in such a way to provide the same static stiffness and the same damping component with the equivalent reference beam on elastic foundation. Numerical examples are used to investigate the effect of the shear on wavenumber and damping for beam with elastic and metamaterial foundations. The effects of engineering

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20

Lee, Usik, In Joon Jang, and Il Wook Park. "Frequency-Domain Spectral Element Model of a Uniform Spinning Shaft." Applied Mechanics and Materials 224 (November 2012): 264–67. http://dx.doi.org/10.4028/www.scientific.net/amm.224.264.

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This paper presents a spectral element model for the spinning uniform shaft represented by the Timoshenko beam model. The bearing-supports are represented by equivalent springs. The variational approach is used to formulate the spectral element model from the frequency-dependent shape functions derived from exact wave solutions to the governing differential equations.

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21

Honickman, Hart. "An Intuitive Derivation of Beam Models of Arbitrary Order." Applied Mechanics 4, no. 1 (2023): 109–40. http://dx.doi.org/10.3390/applmech4010008.

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This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variables, section constants, and section functions that facilitate the development of higher-order beam models that retain a clear philosophical link to classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory. The present beam model is a type of equivalent single layer beam m

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22

Ri, Kwangchol, Poknam Han, Inchol Kim, Wonchol Kim, and Hyonbok Cha. "Stability Analysis of Composite Shafts Considering Internal Damping and Coupling Effect." International Journal of Structural Stability and Dynamics 20, no. 11 (2020): 2050118. http://dx.doi.org/10.1142/s0219455420501187.

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A mathematical model is proposed to analyze the stability of composite shafts, considering the internal damping, transverse shear deformation and Poisson’s coupling effect at the same time. The strain–displacement relations are described using the Timoshenko beam theory, and the strain energy and kinetic energy are expressed using the weak form quadrature element method (QEM), for which each nodal point has 4 degrees of freedom. Then, the motion equation of the system is established using the Lagrange equation. The instability thresholds of the composite shaft are determined using the proposed

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23

Bové, Oriol, Miquel Casafont, Jordi Bonada, and Francesc López‐Almansa. "Comparison between numerical models for unbraced multiple bay pallet racks." ce/papers 6, no. 3-4 (2023): 1597–602. http://dx.doi.org/10.1002/cepa.2312.

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AbstractUnbraced pallet racks are cold‐formed steel structures intended for the storage of products. They are subjected to severe lateral actions, and are particularly instability prone in the down aisle direction. Therefore, their design is compromised and needs of an accurate modelling. In current design practice, models using simplified beam formulations are regularly considered (such as Euler‐Bernoulli or Timoshenko), being them not able to reproduce torsional warping, or cross‐sectional distortion; these phenomena are accounted for indirectly via reduced sectional properties, and in the p

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24

Zhang, Guowei, and Fushou Liu. "Equivalent Dynamic Modeling for the Relative Rotation of Bolted Joint Interface Using Valanis Model of Hysteresis." Machines 11, no. 3 (2023): 342. http://dx.doi.org/10.3390/machines11030342.

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Dynamic modeling of the joint interface is critical to the performance analysis of bolt-jointed structures. In this work, an equivalent modeling method was presented for modeling the relative rotation of the joint interface in bolt-jointed beam structures. As the transverse vibration of the studied structure is closely related to the rotation of the joint, which is different from previous studies that focused on the tangential slip of the joint interface, the Valanis model is used to model the relative rotation of the joint. In addition, the shear deformation and rotational inertia of the beam

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25

Hedayati, Reza, Naeim Ghavidelnia, Mojtaba Sadighi, and Mahdi Bodaghi. "Improving the Accuracy of Analytical Relationships for Mechanical Properties of Permeable Metamaterials." Applied Sciences 11, no. 3 (2021): 1332. http://dx.doi.org/10.3390/app11031332.

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Permeable porous implants must satisfy several physical and biological requirements in order to be promising materials for orthopaedic application: they should have the proper levels of stiffness, permeability, and fatigue resistance approximately matching the corresponding levels in bone tissues. This can be achieved using designer materials, which exhibit exotic properties, commonly known as metamaterials. In recent years, several experimental, numerical, and analytical studies have been carried out on the influence of unit cell micro-architecture on the mechanical and physical properties of

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26

Ding Shuangjiang, Song Leipeng, Wang Taoxi, and Shen Xing. "Mechanical performance study of high flexibility arrow-shaped concave arc bottoms negative Poisson's ratio honeycomb structure." International Journal of Science and Research Archive 13, no. 1 (2024): 2122–35. http://dx.doi.org/10.30574/ijsra.2024.13.1.1882.

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A novel negative Poisson's ratio honeycomb structure with arrow-shaped concave arc bottoms was presented in this paper. The analytical formulas for the equivalent elastic modulus, equivalent Poisson's ratio, and equivalent density were derived based on the theory of the Timoshenko beam under small static deformations and verified by experiments and finite element simulations. Comparative analysis with common negative Poisson's ratio honeycomb structures revealed that the arrow-shaped concave arc bottom structure exhibits superior deformability under load. Experimental results showed that the e

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27

Bozyigit, Baran. "Transfer matrix formulation for dynamic response of Timoshenko beams resting on two-parameter elastic foundation subjected to moving load." Journal of Structural Engineering & Applied Mechanics 4, no. 2 (2021): 99–110. http://dx.doi.org/10.31462/jseam.2021.04099110.

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In this study, the dynamic response of beams resting on two-parameter elastic foundation subjected to moving load is investigated by using the transfer matrix method (TMM). The Timoshenko beam theory (TBT) which considers shear deformation and rotational inertia is used to model the beam. The two-parameter elastic foundation model is selected as Pasternak foundation that takes into account a shear layer at the end of linear springs of Winkler foundation. The TMM which uses the relation between analytically obtained state vectors of each end of the beam is applied to solve the free vibration pr

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28

Zhang, Wukun, Jian Zhao, Yonghua Tan, Yushan Gao, Jun Wang, and Xiaoliang Geng. "Study on the Shear Modulus Based Equivalent Homogenization Methods of Multi-Layer BCC Lattice Sandwich." Materials 15, no. 4 (2022): 1341. http://dx.doi.org/10.3390/ma15041341.

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In this paper, the shear modulus based equivalent homogenization methods of multi-layer BCC (body-centered cubic) lattice sandwich structures have been studied using analytical, experimental, and finite element methods. In the analytical approach, the multiple strut-deformation patterns were introduced in the derivations of the shear modulus based on Euler–Bernoulli beam theory and Timoshenko beam theory according to different boundary conditions. The analytical shear modulus of three types of rectangle shaped sandwich BCC lattice structures was derived. Finite element models of the BCC lattic

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29

Kufner, Tobias, Günter Leugering, Johannes Semmler, Michael Sting, and Christoph Strohmeyer. "Simulation and structural optimization of 3d Timoshenko beam networks based on fully analytic network solutions." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 6 (2018): 2409–31. http://dx.doi.org/10.1051/m2an/2018065.

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This article is concerned with the efficient and accurate simulation and optimization of linear Timoshenko beam networks subjected to external loads. A solution scheme based on analytic ansatz-functions known to provide analytic solutions for the deformation and rotation of a single beam with given boundary data is extended to the full network. It is demonstrated that the analytic approach is equivalent to a finite element (FE) method where only one element with a suitably chosen shape function per beam is required. The solution of the FE-type system provides analytic solutions at the nodes, f

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30

Yang, Xiao, Jin Huang, and Yu Ouyang. "Bending of Timoshenko beam with effect of crack gap based on equivalent spring model." Applied Mathematics and Mechanics 37, no. 4 (2016): 513–28. http://dx.doi.org/10.1007/s10483-016-2042-9.

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31

Piccardo, G., F. Tubino, and A. Luongo. "Equivalent Timoshenko linear beam model for the static and dynamic analysis of tower buildings." Applied Mathematical Modelling 71 (July 2019): 77–95. http://dx.doi.org/10.1016/j.apm.2019.02.005.

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32

Faghidian, S. Ali. "Flexure mechanics of nonlocal modified gradient nano-beams." Journal of Computational Design and Engineering 8, no. 3 (2021): 949–59. http://dx.doi.org/10.1093/jcde/qwab027.

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Abstract Two frameworks of the nonlocal integral elasticity and the modified strain gradient theory are consistently merged to conceive the nonlocal modified gradient theory. The established augmented continuum theory is applied to a Timoshenko–Ehrenfest beam model. Nanoscopic effects of the dilatation, the deviatoric stretch, and the symmetric rotation gradients together with the nonlocality are suitably accommodated. The integral convolutions of the constitutive law are restored with the equivalent differential model subject to the nonclassical boundary conditions. Both the elastostatic and

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33

Ma, Haiying, Zhen Cao, Xuefei Shi, and Junyong Zhou. "Dynamic Amplification Factor of Shear Force on Bridge Columns under Impact Load." Shock and Vibration 2019 (March 10, 2019): 1–14. http://dx.doi.org/10.1155/2019/9483246.

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Shear failure is a common mode for bridge column collapse during a vehicle-column collision. In current design codes, an equivalent static load value is usually employed to specify the shear capacity of bridge columns subject to vehicle collisions. But how to consider the dynamic effect on bridge columns induced by impact load needs further research. The dynamic amplification factor (DAF) is generally used in the analysis and design to include the dynamic effect, which is usually determined using the equivalent single degree of freedom (SDOF) method. However, SDOF method neglects the effect of

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34

Chen, Xia-Chun, Zhen-Hu Li, Francis T. K. Au, and Rui-Juan Jiang. "Flexural Vibration of Prestressed Concrete Bridges with Corrugated Steel Webs." International Journal of Structural Stability and Dynamics 17, no. 02 (2017): 1750023. http://dx.doi.org/10.1142/s0219455417500237.

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Prestressed concrete bridges with corrugated steel webs have emerged as a new form of steel-concrete composite bridges with remarkable advantages compared with the traditional ones. However, the assumption that plane sections remain plane may no longer be valid for such bridges due to the different behavior of the constituents. The sandwich beam theory is extended to predict the flexural vibration behavior of this type of bridges considering the presence of diaphragms, external prestressing tendons and interaction between the web shear deformation and flange local bending. To this end, a [Form

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35

Sinha, Sunil K. "Combined Torsional-Bending-Axial Dynamics of a Twisted Rotating Cantilever Timoshenko Beam With Contact-Impact Loads at the Free End." Journal of Applied Mechanics 74, no. 3 (2006): 505–22. http://dx.doi.org/10.1115/1.2423035.

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In this paper, consideration is given to the dynamic response of a rotating cantilever twisted and inclined airfoil blade subjected to contact loads at the free end. Starting with the basic geometrical relations and energy formulation for a rotating Timoshenko beam constrained at the hub in a centrifugal force field, a system of coupled partial differential equations are derived for the combined axial, lateral and twisting motions which includes the transverse shear, rotary inertia, and Coriolis effects, as well. In the mathematical formulation, the torsion of the thin airfoil also considers a

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36

Gubran, H. B. H., S. P. Singh, and K. Gupta. "Stresses in Composite Shafts Subjected to Unbalance Excitation and Transmitted Torque." International Journal of Rotating Machinery 6, no. 4 (2000): 235–44. http://dx.doi.org/10.1155/s1023621x00000221.

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In the present study, stress analysis of fiber reinforced thin composite shafts subjected to unbalance excitation and steady torque, is carried out. Shafts of uniform as well as variable wall thickness are considered. The shaft is modeled as a simply supported Timoshenko beam in which shear deformation, rotary inertia and gyroscopic effects have been included. Modified equivalent modulus beam theory has been adopted. Rayleigh-Ritz displacements are used for deriving the solution equations. Shafts with a uniform wall thickness, and with variable wall thickness in which the thickness is varied a

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37

Dai, Liangcheng, Maoru Chi, Hongxing Gao, and Jianfeng Sun. "An Investigation into the Modeling Methodology of the Coil Spring." Shock and Vibration 2020 (June 24, 2020): 1–13. http://dx.doi.org/10.1155/2020/8814332.

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The coil spring is an important element in the suspension system of railway vehicles, and its structural vibration caused by the mass distribution can deteriorate the dynamic performance of the vehicle. However, the coil spring is usually modelled as a simple linear force element without considering the dynamic characteristics in multibody dynamic simulations of railway vehicles. To integrate the dynamic characteristics of the coil spring into the simulation, three equivalent dynamic models of the coil spring are established by treating the coil spring as multimass spring series, Timoshenko be

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38

Mamandi, Ahmad, and Mohammad H. Kargarnovin. "Nonlinear Dynamic Analysis of an Inclined Timoshenko Beam Subjected to a Moving Mass/Force with Beam’s Weight Included." Shock and Vibration 18, no. 6 (2011): 875–91. http://dx.doi.org/10.1155/2011/794254.

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In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic ma

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39

Sosnowski, Wlodzimierz. "Simplified Elastic-Plastic Analysis of Stiffened Plates and Space Frames." International Journal of Space Structures 3, no. 1 (1988): 1–14. http://dx.doi.org/10.1177/026635118800300101.

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In this paper two algorithms are presented for approximate nonlinear analysis of stiffened plates subjected to lateral and/or in-plane loads. The stiffened plate is treated either as an equivalent orthotropic plate or as a space frame. The last case corresponds to a discrete beam idealization in which the plate is represented by effective flanges acting together with the stiffeners according to simple beam theory. For plane cases local buckling phenomena are incorporated into the frame model. Three points are believed to be new in this paper: — comparisons between the two models in nonlinear r

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Downs, B. "An equivalent inertia matrix for a segment of a uniform Timoshenko beam of any geometry and material." Journal of Sound and Vibration 105, no. 1 (1986): 109–20. http://dx.doi.org/10.1016/0022-460x(86)90224-5.

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Mikhasev, Gennadii I., and Nguen D. Le. "Asymptotic model of long-wave vibrations of an ultrathin strip-beam taking into account surface effects." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 11, no. 3 (2024): 557–69. http://dx.doi.org/10.21638/spbu01.2024.312.

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The paper is concerned with the derivation of asymptotically consistent equations governing long-wave vibrations of an ultrathin elastic strip-beam taking into account surface effects within the framework of the Gurtin-Murdoch theory of the surface elasticity. Two dimensional equations of motion of an elastic isotropic medium are used as the initial ones. In the general case, the strip-beam is under the action of variable unsteady surface forces. The presence of residual shear stresses is assumed on the face surfaces. The ratio of the strip thickness to the characteristic length of bending def

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Guesmia, Aissa. "Decay rates for two Cauchy thermoelastic laminated Timoshenko problems of type III with interfacial sli." Electronic Journal of Differential Equations 2022, no. 01-87 (2022): 02. http://dx.doi.org/10.58997/ejde.2022.02.

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In this article we study the decay of solutions for two systems of laminated Timoshenko beams with interfacial slip, in the whole space \(\mathbb{R}\) subject to a thermal effect of type III acting only on one component.When the thermal effect acts via the second or third component of the laminatedTimoshenko beam (rotation angle displacement or dynamic of the slip),we prove that both systems are polynomially stable. Also we obtain stability estimates in the \(L^2 (\mathbb{R})\)-norm of solutions and their higher order derivatives with respect of the space variable. The decay rates, and the abs

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Yang, Ta Chung, and Ying An Tsai. "Experimental Modeling Using Pseudo Mode Shape Method." Applied Mechanics and Materials 328 (June 2013): 552–57. http://dx.doi.org/10.4028/www.scientific.net/amm.328.552.

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The foundations of most large industrial machines are complicated in configuration and shape that result in difficulties of modal testing and finite element modeling. Pseudo Mode Shape Method (PMSM) needs only the measurements of frequency response functions at the joint interfaces of the substructure and the mother structure to develop the equivalent dynamic matrices (called the pseudo matrices) of mass, damping, and stiffness of the substructure, which greatly simplifies the modeling procedure of the complicated substructure. Experimental validation of PMSM was conducted by modeling the foun

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Michalczyk, K. "Natural transverse vibrations of helical springs in sections covered with elastic coatings." Bulletin of the Polish Academy of Sciences Technical Sciences 65, no. 6 (2017): 949–59. http://dx.doi.org/10.1515/bpasts-2017-0102.

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AbstractIt has been demonstrated in previous studies that local elastomer coatings covering the end coils of helical springs can efficiently reduce the amplitudes of circum-resonant vibrations in such springs. The analysis of the influence that elastic coatings have on the frequencies and modes of natural transverse vibrations of springs is presented in this paper. The concept of the equivalent beam of the Timoshenko type is utilized in calculations of the frequencies and modes of transverse vibrations. The model developed allows users to determine the frequencies and modes of symmetric as wel

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Wang, Li, Donghui Cheng, Enxiang Qu, Daoming Zhang, and Chun Lv. "Calculation of Additional Internal Forces in Post-Tensioned Prestressed Concrete Frame Columns Based on Equivalent Lateral Stiffness." Buildings 12, no. 5 (2022): 644. http://dx.doi.org/10.3390/buildings12050644.

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The additional internal forces in vertical members caused by prestressed tendons are typically overlooked in the design of post-tensioned prestressed concrete. A calculation method for additional internal forces in single-story multi-span prestressed concrete frame columns based on equivalent lateral stiffness is proposed in this paper. The slope-deflection equation for the bar element was presented using Timoshenko beam assumptions, taking into account the influence of shear and bending deformations. Subsequently, the concept of equivalent lateral stiffness and calculation equations were prop

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Zhou, Yong, Timo Nyberg, Gang Xiong, Shi Li, Hongbo Zhou, and Sen Bao. "Analytical Solution of Thick Piezoelectric Curved Beams with Variable Curvature Considering Shearing Deformation." International Journal of Applied Mechanics 09, no. 01 (2017): 1750006. http://dx.doi.org/10.1142/s1758825117500065.

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In this paper, an analytical method based on Timoshenko theory is derived for obtaining the in-plane static closed-form general solutions of deep curved laminated piezoelectric beams with variable curvatures. The equivalent modulus of elasticity is utilized to take into account the material couplings in the laminated beam. The linear piezoelectric effect is considered to develop the static governing equations. The governing differential equations are formulated as functions of the angle of tangent slope by introducing the coordinate system defined by the arc length of the centroidal axis and t

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Su, Ao, Min Zhang, Wei Shang, and Qiqi Wang. "Transient Horizontal Response of a Pipe Pile in Saturated Soil with a Flexible Support at the Pile Head." Applied Sciences 15, no. 2 (2025): 682. https://doi.org/10.3390/app15020682.

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This study examines the horizontal transient response of pipe piles in saturated soil, assuming a two-stage equivalent linear relationship between the bending moment and the rotation at the pile head. The potential function is introduced, and the three-dimensional wave equation for saturated soils is decoupled using operator decomposition and the method of separation of variables. By applying the appropriate initial and boundary conditions, the horizontal lateral forces on the pile from both the surrounding soil and the soil within the pile shaft are calculated. The pipe pile is modeled as a T

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Samadzad, M., R. Rafiee-Dehkharghani, and A. J. Aref. "A Joint-Based Systematic Wave-Propagation Approach for Forced Vibration Analysis of Large Waveguide Systems." International Journal of Structural Stability and Dynamics 19, no. 07 (2019): 1950075. http://dx.doi.org/10.1142/s0219455419500755.

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This paper describes an analytical and numerical continuous wave-based approach for the forced vibration analysis of large waveguide systems. With Timoshenko beam theory as the basis for modeling wave propagation in the waveguides, the refraction of waves at discontinuities is studied analytically. Within this context, the refraction of waves at multi-member joints is formulated. In addition, a joint-based procedure is introduced to assemble analytical joint equations in the global system matrix. The joint-based approach is mathematically equivalent with the existing element-based approaches b

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Silva, F. G. A., M. F. S. F. de Moura, N. Dourado, et al. "Mode I fracture characterization of human bone using the DCB test." International Journal of Structural Integrity 6, no. 3 (2015): 355–66. http://dx.doi.org/10.1108/ijsi-05-2014-0023.

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Purpose – Fracture characterization of human cortical bone under pure mode I loading was performed in this work. The purpose of this paper is to validate the proposed test and procedure concerning fracture characterization of human cortical bone under pure mode I loading. Design/methodology/approach – A miniaturized version of the double cantilever beam (DCB) test was used for the experimental tests. A data reduction scheme based on crack equivalent concept and Timoshenko beam theory is proposed to overcome difficulties inherent to crack length monitoring during the test. The application of th

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Zhang, Huijie, Jun Zha, Chao Du, Hui Liu, Yang Li, and Dun Lv. "Variable-Coefficient Dynamic Modeling Method for a Ball Screw Feed System in the No-Extra-Load Running State." Processes 11, no. 3 (2023): 793. http://dx.doi.org/10.3390/pr11030793.

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In a ball screw feed system of high-speed/high-acceleration machine tools, large frictional and inertial forces may change the real contact state of the kinematic joints, resulting in changes in the contact and transmission stiffnesses and, hence, changes in the dynamic characteristics of the system. In this study, a variable–coefficient dynamic modeling method for a ball screw feed system is proposed, considering the influence of changes in the no-extra-load running states, such as position, speed, and acceleration. Based on Timoshenko beam elements with two nodes and four DOFs, an equivalent

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