Topic
Timoshenko beam theory
About: Timoshenko beam theory is a research topic. Over the lifetime, 9426 publications have been published within this topic receiving 200570 citations.
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TL;DR: In this paper, the free vibration frequencies of Timoshenko beams on two-parameter elastic foundations were examined and two variants of the equation of motion were deduced, in which the second foundation parameter is a function of the total rotation of the beam or a function due to bending only, respectively.
100 citations
TL;DR: In this article, the authors used the wavelet transform to analyze the mode shape of a Timoshenko beam and demonstrated that the crack position can be detected by this method even though the crack is very small.
100 citations
TL;DR: In this article, non-linear and linearized equations are derived for the in-plane stretching and bending of thin-walled cylindrical beams made of a membrane and inflated by an internal pressure.
Abstract: The non-linear and linearized equations are derived for the in-plane stretching and bending of thin-walled cylindrical beams made of a membrane and inflated by an internal pressure. The Timoshenko beam model combined with the finite rotation kinematics enables one to correctly account for the shear effect and all the non-linear terms in the governing equations. The linearization is carried out around a pre-stressed reference configuration which has to be defined as opposed to the so-called natural state. Two examples are then investigated: the bending and the buckling of a cantilever beam. Their analytical solutions show that the inflation has the effect of increasing the material properties in the beam solution. This solution is compared with the three-dimensional finite element analysis, as well as the so-called wrinkling pressure for the bent beam and the crushing force for the buckled beam. New theoretical and numerical results on the buckling of inflatable beams are displayed.
99 citations
TL;DR: In this article, the effects of different sandwich beam models, boundary conditions, gradient index, the velocity, excitation frequency and the phase angles of the two successive harmonic loads, and the distance between the loads on the mechanical behavior of sandwich beams are discussed in detail.
Abstract: This paper examines static, free and forced vibration of functionally graded (FG) sandwich beams under the action of double moving harmonic loads travelling with constant velocities using Timoshenko beam theory (TBT). Three different sandwich beam models with various cross-sectional shape and various boundary conditions are considered. It is assumed that in FG part of sandwich beams, the material properties vary continuously through the thickness of the beam according to simple power-law form. The problem is formulated based on the energy approach. For this purpose, the unknown displacement functions are approximated by using the simple polynomials together with the auxiliary functions for satisfying the essential boundary conditions. The equations of the motion are obtained by using the Lagrange's equations, and solved with the help of the implicit time integration method of Newmark-. In this study, the effects of the different sandwich beam models, boundary conditions, gradient index, the velocity, excitation frequency and the phase angles of the two successive harmonic loads, and the distance between the loads on the mechanical behavior of sandwich beams are discussed in detail. At the same time, extensive static and free vibration results are presented to check the reliability of the present formulation. Good agreement is observed.
99 citations
TL;DR: In this paper, a multibeam shear model was proposed to predict the fundamental and secondary resonant frequencies of cantilever graphene nanostrips with different layer number n and different nanostrip length L.
Abstract: Graphene nanostrips with single or few layers can be used as bending resonators with extremely high sensitivity to environmental changes. In this paper we report molecular dynamics (MD) simulation results on the fundamental and secondary resonant frequencies f of cantilever graphene nanostrips with different layer number n and different nanostrip length L . The results deviate significantly from the prediction of not only the Euler–Bernoulli beam theory ( f ∝ nL −2 ), but also the Timoshenko's model. Since graphene nanostrips have extremely high intralayer Young's modulus and ultralow interlayer shear modulus, we propose a multibeam shear model (MBSM) that neglects the intralayer stretch but accounts for the interlayer shear. The MBSM prediction of the fundamental and secondary resonant frequencies f can be well expressed in the form f − f mo n o ∝[( n –1)/ n ] b L −2(1− b ) , where f mono denotes the corresponding resonant frequency as the layer number is 1, with b =0.61 and 0.77 for the fundamental and secondary resonant modes. Without any additional parameters fitting, the prediction from MBSM agrees excellently with the MD simulation results. The model is thus of importance for designing multilayer graphene nanostrips based applications, such as resonators, sensors and actuators, where interlayer shear has apparent impacts on the mechanical deformation, vibration and energy dissipation processes therein.
99 citations