Torsional Vibrations of Pretwisted Cantilever Plates

Abstract

A pretwisted cantilever plate is treated as a thin shallow shell. Its potential and kinetic energies in torsional vibration are determined by assuming an appropriate displacement field. Applying Hamilton’s principle, the problem is reduced to a fourth-order ordinary differential equation with constant coefficients, which is solved to obtain the first four torsional frequencies of vibration. Plates of aspect ratios varying from 1.0 to 8.0 are analyzed with pretwist angles varying from 0 to 90 deg. Results of the present analysis are compared with existing theoretical and experimental results.