Vibration Analysis of a Thin Circular Plate with Several Clamped Points

The natural frequencies and the mode shapes of a simply supported thin circular plate with several c1amped points are determined by two methods. A partial differential equation is solved using Fourier series of Dirac's delta function first， and then a partial integro-differential equation is solved using eigenfunctions and eigenfrequencies of a simply supported thin circular plate. If the bending moments at the c1amped points for free vibration are considered as harmonically excitation moments with unknown amplitudes， a periodic solution of forced vibration of a simply supported thin circular plate is obtained. Using the constraint conditions that the slopes of deflection must be zero at the c1amped points， simultaneous equations with respect to the unknown amplitudes of moments are obtained. The frequency equation is obtained from a necessary and sufficient condition for existence of the non-trivial solutions