Forced transverse vibrations of an elastically connected complex rectangular simply supported double-plate system

The paper deals with forced transverse vibrations of an elastically connected rectangular double-plate system. This complex continuous system can represent a certain simplified model of a three-layered structure consisting of two parallel thin plates separated by an elastic massless layer of a Winkler type. Undamped motion of the system excited by arbitrarily distributed continuous loadings subjected transversely to both plates are governed by a linear set of two coupled non-homogeneous partial differential equations, based on the Kirchhoff–Love plate theory. The forced vibration problem is solved generally by the application of the modal expansion method in the case of simply supported boundary conditions for plates. On the basis of general solutions obtained, three particular cases of the action of exciting stationary harmonic loads are considered. An analysis of harmonic responses of the system makes it possible to determine conditions of resonance and dynamic vibration absorption. A numerical example is given to illustrate the theory presented.