Free vibration analysis of beams with variable flexural rigidity resting on one or two parameter elastic foundations using finite difference method

چکیده مقاله

In this paper, the Finite Difference Method (FDM) is applied to evaluate natural frequencies of non-prismatic beams, with different boundary conditions and resting on variable one or two parameter elastic foundations. Finite difference method is one of the most powerful numerical techniques for solving differential equations especially with variable coefficients. Between various computational methods to solve the motion equations, this method requires a minimum of computing stages and is therefore very suitable approach for engineering analysis where the exact solution is very difficult to obtain. The main idea of this method is replacing derivatives present in the free vibration equation and boundary condition equations with finite difference expressions. The natural frequencies are determined by solving the eigenvalue problem of the obtained algebraic system resulting from FDM expansions. In order to illustrate the correctness and performance of the method, a comprehensive numerical example of non-uniform beams is presented. The results are compared with the finite element results using Ansys software and other available numerical and analytical solutions.