Abstract
In this paper, the free transverse vibrations of a system of two rectangular simply supported thin plates connected by a homogeneous Winkler elastic layer are investigated analytically. The small vibrations of the system are described by a set of two partial differential equations, based on the Kirchhoff–Love plate theory. Next, the homogeneous equations of motion are solved by using the classical Navier method. The natural frequencies of the system in the form of two infinite sequences are determined and the corresponding mode shapes of vibration are shown. As a consequence, an elastically connected double-plate complex system executes two kinds of the free vibrations: synchronous and asynchronous. The initial-value problem is then considered to find the final form of the free vibrations. The theoretical analysis presented is illustrated by a numerical example, in which the free vibrations of a system of two identical plates are discussed in detail.
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