Dynamic stiffness analysis of axially loaded non-uniform Timoshenko columns

Abstract

A dynamic stiffness method is introduced to analyze axially loaded non-uniform Timoshenko columns. A dynamic stiffness matrix is formed by frequency-dependent shape functions which are exact solutions of the governing differential equations. It eliminates spatial discretization errors and is capable of predicting a number of natural modes by means of a small number of degrees of freedom. The method is now widely used in various dynamic problems. In this study the two coupled governing differential equations of a non-uniform column are solved by power series. The natural frequencies of the non-uniform beams under axial force can be found by equating to zero the determinant of the dynamic stiffness matrix of the system. Numerical examples are studied and the results are compared with those obtained by finite element method.