Comprehensive exact solutions for free in-plane vibrations of orthotropic rectangular plates

All possible exact solutions are successfully obtained for the first time in terms of 10 sets of distinct eigensolutions for the free in-plane vibration of orthotropic rectangular plates when two opposite plate edges are either type of simple support, the other two edges are any combination of classical edge conditions. The exact solutions are validated through both mathematical proof and comparisons with the solutions of differential quadrature method. Some unusual phenomena are revealed in free in-plane vibrations of rectangular plates due to one of the eigenvalues being zero. This work constitutes a natural extension of very recent corresponding work for isotropic rectangular plates by the same authors. Moreover, this work substantially simplified both solution forms and solving procedure of the early work. It is expected that results tabulated here can serve as the benchmarks for the validation of the numerical methods.