Free vibration analysis of rectangular orthotropic cantilever plates with point supports.

Abstract

The free vibration analysis of rectangular plates has been of interest to many scholars and practitioners over the years due to their wide range of applications. However, most of the studies involve the typical case of isotropy. A study has been done in the analysis of free vibration of orthotropic cantilever plates with internal point supports. The analysis makes use of the Superposition Method which, by superimposing appropriate building blocks, can provide "exact" analytical solution to this problem of orthotropy. In each case of symmetric and antisymmetric vibration modes under study, three different plate problems whose Levy-type solutions can be obtained, are superimposed. The constants in each solution, created during their boundary condition formulations, are adjusted in such a way so their combination would provide boundary conditions the same to those required for the cantilever plate. Upon superimposing, an eigenvalue matrix is created which allows the eigenvalues to be determined. Accuracy of the resultant eigenvalues is verified by recognising that the governing differential equation is satisfied exactly and that the required plate boundary conditions are satisfied to certain desired degree of exactitude. The objective of this thesis is to describe the necessary modifications to adapt the superposition method to orthotropic plate problems, and to show the mathematical procedures employed in the analysis. In addition, the results of some representative frequency and mode shape studies will be presented which include a wide range of plate geometries and various levels of orthotropy.