Dynamic stiffness analysis of non-uniform Timoshenko beams

Abstract

A dynamic stiffness method is introduced to analyze non-uniform Timoshenko beams with various boundary conditions. A dynamic stiffness matrix is formed by using frequency dependent shape functions which are exact solutions of the governing differential equations. This eliminates spatial discretization error and is capable of predicting many natural modes with use of a small number of degrees of freedom. The method is now widely used in various dynamic problems [1-4]. In this study it is not necessary to reduce the two coupled governing differential equations into one equation, as has been done by many authors [5-8]. The natural frequencies of the non-uniform beams can be found by equating to zero the determinant of the dynamic stiffness matrix of the system. Several cases are studied and the results are compared with those obtained by the finite element method.