Damped forced vibrations of an elastically connected double-membrane system

The purpose of the present paper is to consider theoretically damped forced transverse vibrations of an elastically connected rectangular double-membrane system. The system is treated as two viscoelastic membranes joined by a Kelvin-Voigt viscoelastic layer. Applying the modal expansion method, exact analytical solutions of damped forced responses for a simplified model of this system subjected to arbitrarily distributed transverse continuous loads are determined in the case of arbitrary magnitude of linear viscous damping. Nine possible different solutions obtained are described by the combinations of time functions expressing the damped motions for undercritical, critical and overcritical damping cases, according to the mutual relations between physical parameters of the system.