Free Axisymmetric Flexural Vibrations of Circular Plate with Symmetrically Varying Mechanical Properties Supported on Elastic Foundation

The subject of the paper is a circular plate with clamped edge supported on elastic foundation. Mechanical properties of the plate symmetrically vary in its thickness direction. Free axisymmetric flexural vibration problem of the plate with consideration of the shear effect is analytically studied. Two partial differential equations of motion based on the Hamilton principle are obtained. The system of equations is analytically solved and the fundamental natural frequency of axisymmetric vibration for example plates is derived.