Free Vibration of Isotropic Rectangular Beam Based on Orthogonal Finite Element Method

Abstract

Present work deals with free vibration of isotropic rectangular beam subject to various sets of boundary conditions. Governing differential equation has been solved by finite element method where the shape function has been taken as orthogonal polynomials generated from simple algebraic polynomials. Orthogonal polynomials are obtained first by means of Gram-Schmidt orthogonalization procedure. The generalized eigenvalue problem for free vibration is obtained after finding the concerned stiffness and mass matrices from orthogonal finite element method. We have also considered various types of discretizations in the beam element for the simulation. Results for eigenfrequencies are incorporated after checking the test of convergence and comparison of present results with available literature in special cases.