Free In-Plane Vibration Analysis of Annular Plates with General Boundary Conditions

An analytical method is derived for the free in-plane vibration analysis of annular plates with general boundary conditions. Under this framework, all the classical homogeneous boundary conditions can be treated as the special cases when the stiffness for each restraining springs is equal to either zero or infinity. The improved Fourier series solutions for the in-plane vibrations are obtained by employing the Rayleigh-Ritz method. A numerical example is presented to demonstrate the accuracy and reliability of the current method.