Free vibration of circular footing on elastic foundations

The free vibration of a circular plate on an elastic foundation is analyzed by using Vlasov's two-parameter model. The natural frequencies of the system under axisymmetric conditions are determined. In the region of the plate, the general solution is represented by Bessel functions. Modified wave equations are used to predict the harmonic motion of the elastic foundation. Since the region outside of the plate is infinite, a reflected wave is not produced, thereby eliminating the need to consider a wave moving toward the plate. Finally, the effects of various parameters of the plate and the foundation on the natural frequencies system are discussed.