Natural Vibrations of a Circular Five-Layer Plate Caused by Initial Deflection

This paper presents a formulation of an initial-boundary value problem for the natural vibrations of a five-layer circular plate symmetrical in thickness, arising from an initial deflection. The central and outer layers are assumed to be thin load-bearing, and the deformation in them is described by Kirchhoff’s hypotheses. The two relatively thick cores are lightweight, so that Timoshenko’s hypothesis is valid for them. A system of partial differential equations of motion is obtained using a variational method. An analytical solution to the problem is obtained by expanding the sought-for displacements into a series of orthonormal eigenfunctions. A numerical analysis of the resulting solution is performed.