Analytical analysis of the free vibration of partially clamped cantilever plates.

Abstract

The method of superposition is used to analyze the free vibration of thin rectangular plates, partially clamped along one edge and free everywhere else. This study has been undertaken because of interest in the dynamic behaviour of electronic circuit boards which are sometimes given support of this nature. This problem is not known to have been studied before using an analytical type method. Eight building blocks are superimposed to obtain the final solution. Each building block is solved individually using the Levy-type solution. A detailed mathematical development of the solution is shown for each building block in dimensionless form. The natural frequencies and mode shapes for plates with varying aspect ratios and clamped lengths can be found using this method. Eigenvalues are shown to converge and tabulated values are given to at least three digit accuracy. Frequencies and mode shapes agree very well with experimentally found results and with results found using a commercially used finite element method software package.