Effect of boundary conditions on the non-linear forced vibration response of isotropic plates

Abstract

The effect of boundary conditions on the linear and nonlinear steady state forced vibration response of rectangular isotropic plates have been investigated. For thin components subjected to dynamic forces the amplitude of vibration is comparable to its thickness which requires inclusion of nonlinear terms in the strain displacement relation. In the present work the non-linear governing equations of motion have been obtained using standard finite element procedure based on displacement field of FSDT. The governing equation of motion is solved using modified shooting method. The unstable portions of frequency response curves are obtained using continuation algorithm [1]. The non-linear responses are compared with linear response and very large difference between the two has been obtained. Unlike frequency domain methods such as Harmonic balance and IHB the present method does not require any assumption on participating modes. The time history, phase plane plots and FFT of the response have also been obtained to explain the physics of the peculiar nature of the nonlinear response.