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2020
Unlike the Bernoulli beam formulation, the Timoshenko beam formulation accounts for transverse shear deformation. It is therefore capable of modeling thin or thick beams. In this chapter we perform the analysis of Timoshenko beams in static bending, free vibrations and buckling. We present the basic formulation and show how a MATLAB code can accurately
Ferreira A. J. M., Fantuzzi N.
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Unlike the Bernoulli beam formulation, the Timoshenko beam formulation accounts for transverse shear deformation. It is therefore capable of modeling thin or thick beams. In this chapter we perform the analysis of Timoshenko beams in static bending, free vibrations and buckling. We present the basic formulation and show how a MATLAB code can accurately
Ferreira A. J. M., Fantuzzi N.
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Vibrations of Tapered Timoshenko Beams in Terms of Static Timoshenko Beam Functions
Journal of Applied Mechanics, 2000In this paper, the free vibrations of a wide range of tapered Timoshenko beams are investigated. The cross section of the beam varies continuously and the variation is described by a power function of the coordinate along the neutral axis of the beam.
Cheung, YK, Zhou, D
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Boundary Control of the Timoshenko Beam
SIAM Journal on Control and Optimization, 1987The paper investigates uniform stabilization of the Timoshenko beam with boundary control. The main result of the first part, established by means of the energy method combined with \(C_ 0\)-semigroup theory, is that the natural energy of the beam decays exponentially fast.
Kim, Jong Uhn, Renardy, Yuriko
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On dynamic optimization of Timoshenko beam
Applied Mathematics and Mechanics, 1983The present paper discusses the minimum weight design problem for Timoshenko and Euler beams subjected to multi-frequency constraints. Taking the simply-supported symmetric beam as an example, we reveal the abnormal characteristics of optimal Timoshenko beams, i.e., the frequency corresponding to the first symmetric vibration mode could be higher than ...
Cheng, Keng-tung, Ding, Hua
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Dynamics of Laminated Timoshenko Beams
Journal of Dynamics and Differential Equations, 2017The authors describe the long-time dynamics of a Timoshenko system consisting of two identical beams joined by a thin adhesive layer. After some transformations, the authors obtain the coupled system of three evolution equations \(\rho w_{tt}+G\varphi _{x}+g_{1}(w_{t})+f_{1}(w,\xi ,s)=h_{1}\), \(I_{\rho }\xi _{tt}-G\varphi -D\xi _{xx}+g_{2}(\xi _{t ...
Feng, B. +3 more
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2021
The Euler-Bernoulli beam theory is based on the fundamental hypothesis that the cross sections remain plane and that the normal hypothesis is valid, i.e. a beam is assumed where shear strains of the cross section are explicitly excluded.
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The Euler-Bernoulli beam theory is based on the fundamental hypothesis that the cross sections remain plane and that the normal hypothesis is valid, i.e. a beam is assumed where shear strains of the cross section are explicitly excluded.
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Journal of Sound and Vibration, 1972
Abstract A Timoshenko beam finite element which is based upon the exact differential equations of an infinitesimal element in static equilibrium is presented. Stiffness and consistent mass matrices are derived. Convergence tests are performed for a simply-supported beam and a cantilever. The effect of the shear coefficient on frequencies is discussed
R. Davis, R.D. Henshell, G.B. Warburton
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Abstract A Timoshenko beam finite element which is based upon the exact differential equations of an infinitesimal element in static equilibrium is presented. Stiffness and consistent mass matrices are derived. Convergence tests are performed for a simply-supported beam and a cantilever. The effect of the shear coefficient on frequencies is discussed
R. Davis, R.D. Henshell, G.B. Warburton
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Journal of Applied Mechanics, 1971
The general problem of Timoshenko beam analysis is solved using the Laplace transform method. Time-dependent boundary and normal loads are considered. It is established that the integrands of the inversion integrals are always single-valued for beams of finite length and modal solutions can always be obtained using the residue theorem.
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The general problem of Timoshenko beam analysis is solved using the Laplace transform method. Time-dependent boundary and normal loads are considered. It is established that the integrands of the inversion integrals are always single-valued for beams of finite length and modal solutions can always be obtained using the residue theorem.
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Free Vibrations of Viscoelastic Timoshenko Beams
Journal of Applied Mechanics, 1971The correspondence principle has been applied to derive the differential equations of viscoelastic Timoshenko beams with external viscous damping. These equations are solved by Laplace transform and boundary conditions are applied to obtain complex frequency equations and mode shapes for beams of any combination of end conditions.
Huang, T. C., Huang, C. C.
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