The Free and damped vibrations of a circular plate with given initial conditions, which is either free or elastically restrained along its outer edge, are discussed using the method developed by Reid and some numerical results are also given.

The vibration of a circular plate has been studied considerably and most of the authors seem to be interested in determining the frequencies of vibration and the nodal patterns. A few investigators have studied the problem of determining the subsequent motion of a thin plate started with some given initial displacement or velocity. Sneddon has attempted this problem, taking into account an approximate boundary condition. Recently Reid has discussed this problem without taking recourse to any approximate boundary condition. He has developed a method of analysis to determine the displacement of a freely vibrating thin circular plate with the given initial conditions, using the norm of the eigen functions.