Dynamic stiffness analysis of thin-walled structures

Abstract

A dynamic stiffness method is introduced to analyse thin-walled structures to reduce spatial discretisation errors. Where harmonic oscillation is concerned, time discretisation errors are also eliminated to give an exact solution in a classic sense. Constant axial forces and in-plane moments are included for dynamic buckling analysis. When warping effects are included, the governing differential equations correspond to a matrix polynomial eigenproblem of order 3 matrices and degree 4. The determinant equation is expanded analytically to give a scalar polynomial equation of degree 12 providing 12 integration constants for the 12 nodal displacements of the thin-walled beam member (excluding the uncoupled axial displacements). The generalised nodal forces are related to the nodal displacements analytically resulting in the exact dynamic stiffness matrix. Numerical examples show that the interaction diagram of natural frequency against the constant in-plane moment do not have monotonic change of slope. This is due to the fact that the constant in-plane moment softens the flexural modes while hardening the torsional modes. Examples on frames are also given.