Computation of free vibration frequencies and mode shapes of cantilever plates with finite discontinuities in properties moving outward from the clamped edge.

Abstract

The study of rectangular cantilever plates with step discontinuities in properties is of interest in many areas of industry. Cantilever plates are assigned different properties to represent change in stiffness and mass creating therefore the concept of step discontinuities in properties. The step discontinuity in properties is best represented by dividing the cantilever plate into separate segments called spans, with each span having its own stiffness and/or mass distribution as one moves outwards from the clamped edge. This thesis presents the concept of dividing the cantilever plate into spans and provides accurate analytical solutions for free vibration frequencies and mode shapes. Chapter 1 introduces the reader to the theory of rectangular plates while chapter 2 concentrates on introducing the general solutions as applied to rectangular plates. Although there is no limit to the number of plate spans to be studied, three and four span cantilever plates were analysed in chapter 3. The computed eigenvalues are validated against previously published uniform rectangular cantilever plate free vibration results. They were found converging to the known values. Free vibration eigenvalues and mode shapes are then calculated for a variety of cantilever plates of different aspect ratios and with different span thicknesses creating a discontinuity in mass and flexural rigidity along the plate. The results are presented in chapter 4 and discussed in chapter 5.