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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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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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2021
This chapter presents the analytical description of thick, or so-called shear-flexible, beam members according to the Timoshenko theory. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, the partial differential equations, which describe the physical problem,
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This chapter presents the analytical description of thick, or so-called shear-flexible, beam members according to the Timoshenko theory. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, the partial differential equations, which describe the physical problem,
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Hybrid laminated Timoshenko beam
Journal of Mathematical Physics, 2017We consider the hybrid laminated Timoshenko beam model. This structure is given by two identical layers uniform on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip.
C. A. Raposo +3 more
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Timoshenko beam finite elements
Journal of Sound and Vibration, 1973During the past few years, a number of different finite elements for Timoshenko beams have been published. These formulations are reviewed and a new element which has three degrees of freedom at each of two nodes is presented. The rates of convergence of a number of the elements are compared by calculating the natural frequencies of two cantilever ...
Thomas, D. L. +2 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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Inhomogeneous Timoshenko beam equations
Mathematical Methods in the Applied Sciences, 1992AbstractThe so‐called Timoshenko beam equation is a good linear model for the transverse vibrations of a homogeneous beam. Following the variational approach of Washizu, the governing equation is deduced in the case when the physical/geometrical parameters of the beam vary along its axis.
AROSIO, Alberto Giorgio +2 more
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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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