Parametrically Excited Stability of a Simply Supported Beam Under Axial Periodic Excitation

Abstract

The parametrically excited stability of beams with multiple mode vibration under general periodic axial excitation is studied and the periodic transverse supports are considered for the first time. The partial differential equation of motion of the beam with spaced supports under axial excitation is given and then converted into ordinary differential equations with periodic parameters by using the Galerkin method. The direct eigenvalue analysis method is applied to solve the parametrically excited stability of the beam described by the differential equations with periodic parameters based on the Fourier expansion and generalized eigenvalue analysis. A track beam with spaced supports under periodic axial excitation is considered. Numerical results on unstable regions are given to illustrate the parametrically excited stability of the beam and the influence of supports and excitation on the stability.