Free Vibration of Circular Plate with Oscillators and Elastic Supports at Arbitrary Positions by Integral Equation Method

The paper concerns on the free vibrations of circular plate with arbitrary number of the elastic supports and the elastically mounted masses at arbitrary positions by using the integral equation method. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first kind, is used to construct the Green's function of circular plates firstly. Then the eigenvalue problem of free vibration of circular plate carrying oscillators and elastic supports at arbitrary positions is transformed into the problem of integral equation by using the superposition theorem and the physical meaning of the Greenpsilas function. And then the eigenvalue problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical examples are presented.