Parametric analysis of axisymmetric vibrations of circular plates on a power-law varying elastic foundation

A parametric study of the free axisymmetric vibrations of a circular plate on a continuous Winkler elastic foundation is carried out. The foundation is assumed to be radially inhomogeneous, with the foundation modulus varying according to a power-law function of the dimensionless radial coordinate. Fundamental solutions of the differential equation governing the vibrations are presented in closed form as absolutely and uniformly convergent double power series. Analytical relationships between the vibration frequencies and the foundation inhomogeneity parameter, as well as the generalized parameter of the mechanical system, are obtained over a wide range of their values. The results obtained can be used in the analysis, design, and optimization of plate structures interacting with a nonhomogeneous elastic foundation.