Vibration of skewed cantilever plates and helicoidal shells

Abstract

Theoretical vibration frequencies and mode shapes are obtained for skewed plates and helicoidal shells with a cantilever boundary. Using Hamilton's law of varying action, a power series solution is developed to obtain converged numerical results for the five lowest frequencies. Effects of geometrical variables such as aspect ratio, sweep angle and shell radius to thickness ratio are investigated. Accuracy of the solution method is substantiated by comparison with existing skewed plate spherical cap, and conical shell results