Three-dimensional exact solutions for the free vibration of laminated transversely isotropic circular, annular and sectorial plates with unusual boundary conditions

New state space formulations for the free vibration of circular, annular and sectorial plates are established by introducing two displacement functions and two stress functions. The state variables can be separated into two independent catalogues and two kinds of vibrations can be readily found. Expanding the displacements and stresses in terms of Bessel functions in the radial direction and trigonometric functions in the circumferential direction, we obtained the exact frequency equation for the free vibration for some uncommon boundary conditions. Numerical results are presented and compared with those of FEM to demonstrate the reliability of the proposed method. A parametric investigation is also performed.