Vibration of simply supported-clamped skew plates at large amplitudest

Abstract

The large amplitude, free, flexural vibration of orthotropic skew plates simply supported along two opposite edges and clamped along the other two are investigated on the basis of an assumed mode shape. The relationship between the amplitude and period is studied for both isotropic and orthotropic skew plates for various aspect ratios and skew angles under two in-plane edge conditions. It is found that the modal equation reduces to the Dufling type equation from which the period of non-linear vibration is found to decrease with increasing amplitude, exhibiting hardening type of non-linearity. The validity of the Berger approximation is investigated for the problem under consideration and this approximation is shown to give reasonably good results.