Analytical solution for free vibration of transversely isotropic sector plates using a boundary layer function

The exact analytical solution based on the Mindlinʹs plate theory is presented for the free vibration of a transversely isotropic sector plate. The plate has simply supported radial edges and arbitrary conditions along the circular edge. By introducing a boundary layer function, the three coupled governing equations of motion have been converted into two uncoupled equations. Solving the uncoupled equations and satisfying the boundary conditions yields an eigenvalue problem for finding the natural frequencies. Non-dimensional frequency parameter is presented for over a wide range of salient (α⩽180) and re-entrant (180<α⩽360) angles, some thickness–radius ratios and different boundary conditions along the circular edge.