Vibration of rectangular plates: fundamental mode and integer multiple of the fundamental period of vibration

Abstract

This paper is concerned with a vibration analysis of the transverse vibrations of rectangular plates with freely-supported boundaries and corners fixed, in an imagistic way, to describe the deformation state for the specific natural frequency and mode shape for each degree-of-freedom. Two materials, i.e. aluminum and steel, showing the homogeneous properties in the direction of plate thickness were chosen. The exact solutions for free vibrations of the homogeneous rectangular plate were obtained and the fundamental mode and integer multiple of the fundamental period of vibration were provided. The comparisons show that the analytical model predicts natural frequencies reasonably well for a rectangular plate.