Non-linear flexural vibration of orthotropic skew plates

Abstract

This report deals with the large amplitude (non-linear) free flexural vibration of thin, elastic, orthotropic skew plates clamped along all four edges. The analysis is based on the non-linear dynamic equations applicable for rectilinearly orthotropic skew plates, derived in terms of the stress function, F, and the lateral displacement, W. Solutions obtained on the basis of assumed vibration modes make use of Galerkin's method. Curves of amplitude versus period for clamped skew plates have been obtained for two types of orthotropy and, in each case, for different aspect ratios and sweep angles of the plate. The corresponding relationship for the isotropic case has also been obtained. The results when specialized for the cases of isotropic skew plates and orthotropic rectangular plates agree well with those in the literature. The results show that the non-linearity is of the "hardening" type, that is, the period of non-linear vibration decreases with increasing amplitude.