Energy analysis of free transverse vibrations of the viso-elastically connected double-membrane system

Abstract

The presented paper deals with the analysis of energy transfer in the viscoelastically connected circular double-membrane system for free transverse vibration of the membranes. The system motion is described by a set of two coupled non-homogeneous partial differential equations. The solutions are obtained by using the method of separation of variables. Once the problem is solved, natural frequencies and mode shape functions are found, and then the form of solution for small transverse deflections of membranes is derived. Using the obtained solutions, forms of reduced kinetic, potential and total energies, as functions of dissipation of the whole system and subsystems, are determined. The numerical examples are given as an illustration of the presented theoretical analysis as well as the possibilities to investigate the influence of different parameters and different initial conditions on the energies transfer in the system.