Benchmark analytic in-plane vibration frequencies of orthotropic rectangular plates

Abstract

The in-plane vibrations of rectangular plates is classic problem in mechanics. It involves the solution of two coupled differential equations with many combinations of possible edge restraints. Exact solution, for some cases, and high accuracy solution for few more cases, have been obtained along the years. In this work a new high accuracy solution, that covers all the possible combinations is presented. It is obtained by using carefully chosen series that solve the coupled partial differential equations of motion, for all possible combinations of edge conditions. Examples of the new solutions are given and compared with other known solutions and with approximate solutions for these cases. Benchmark results are given for square orthotropic plates with all possible combinations of boundary conditions.