Stability boundaries for parametrically excited systems by dynamic stiffness

Abstract

The dynamic stability of skeletal systems subject to harmonic axial forces is of interest. Temporal discretization is achieved by Fourier expansion. The resulting differential equations in spatial co-ordinates alone are solved by the exact frequency-dependent shape functions. The dynamic stability boundaries are determined by studying the free vibration behaviour with periods T and 2T, where T is the period of the harmonic axial force. Since spatial discretization is completely eliminated, many stability boundaries can be determined accurately with the minimum number of elements.