The assessment of soil depth sensitivity to dynamic behavior of the Euler-Bernoulli beam under accelerated moving load

Dynamic behavior is one of the most crucial characters in the railways structures. One of the items which leads to precise identification of the dynamic behavior of railways is the soil depth beneath them. In this paper, an Euler-Bernoulli beam on a finite depth foundation under accelerated moving load is presented. The dynamic equilibrium in the vertical direction is only regarded in accordance with the factor of finite beams. In this study, the dynamic equilibrium of the soil in the vertical direction and the sensitivity of soil depth are considered. The governing equations are simulated by using Fourier transform method. Eventually, by considering the sequences of shear waves, and different kinds of damping, displacement of the beam is obtained for the various acceleration, times and soil depth. As a result, it is shown that, higher acceleration is not dramatically effective on the beam displacement. Also, foundation inertia causes a significant reduction in critical velocity and can augment the beam response

Bending Solution for Simply Supported Annular Plates Using the Indirect Trefftz Boundary Method

This paper presents the bending analysis of annular plates by the indirect Trefftz boundary approach. The formulation for thin and thick plates is based on the Kirchhoff plate theory and the Reissner plate theory. The governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. The Trefftz method employs the complete set of solutions satisfying the governing equation. The main benefit of the Trefftz boundary method is that it does not involve singular integrals because of the properties of its solution basis functions. It can therefore be classified into the regular boundary element method. The present method is simple and efficient in comparison with the other methods. In addition, the boundary conditions can be embedded in this method. Finally, several numerical examples are shown to illustrate the efficiency and simplicity of the current approach

CGO and SNS Optimization Algorithm for the Structures with Discontinuous and Continuous Variables

This study aims to find discontinuous and continuous approaches to reducing the size of planar truss structures with a specified shape and topology. The member’s section area has assumed to be a decision variable, and the objective function is to minimize their weight. The member stresses and node displacements are the constraints that must maintain within the allowed limits for each condition. Chaos game optimization (CGO) and social network search (SNS) algorithms were used to optimize four well-known planar truss structures. In discontinuous-size cases, the results of the social network search (SNS) algorithm are the most cost-effective. However, the results of the chaos game optimization (CGO) algorithm are the most cost-effective in continuous-size cases

An Analytical Solution for Free Vibration of Elastically Restrained Timoshenko Beam on an Arbitrary Variable Winkler Foundation and Under Axial Load

Abstract Natural frequencies are important dynamic characteristics of a structure where they are required for the forced vibration analysis and solution of resonant response. Therefore, the exact solution to free vibration of elastically restrained Timoshenko beam on an arbitrary variable elastic foundation using Green Function is presented in this paper. An accurate and direct modeling technique is introduced for modeling uniform Timoshenko beam with arbitrary boundary conditions. The applied method is based on the Green Function. Thus, the effect of the translational along with rotational support flexibilities, as well as, the elastic coefficient of Winkler foundation and other parameters are assessed. Finally, some numerical examples are shown to present the efficiency and simplicity of the Green Function in the new formulation

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Abstract Natural frequencies are important dynamic characteristics of a structure where they are required for the forced vibration analysis and solution of resonant response. Therefore, the exact solution to free vibration of elastically restrained Timoshenko beam on an arbitrary variable elastic foundation using Green Function is presented in this paper. An accurate and direct modeling technique is introduced for modeling uniform Timoshenko beam with arbitrary boundary conditions. The applied method is based on the Green Function. Thus, the effect of the translational along with rotational support flexibilities, as well as, the elastic coefficient of Winkler foundation and other parameters are assessed. Finally, some numerical examples are shown to present the efficiency and simplicity of the Green Function in the new formulation