Natural frequencies of a linearly tapered non-homogeneous isotropic elastic circular plate resting on an elastic foundation

An analysis is presented here for the design of engineering systems where composite materials and non-uniform structures are used. A simple model for free vibrations of a non-homogeneous isotropic elastic circular plate of linearly varying thickness resting on an elastic foundation is considered. The governing differential equation of motion is solved by the Frobenius method. The frequencies, deflections and moments corresponding to the first five modes of vibration are computed for clamped and simply supported edge conditions for various values of taper constant, non-homogeneity parameter and foundation modulus.