Free transverse vibrations of an elastically connected rectangular plate–membrane complex system

This paper theoretically analyzes undamped free transverse vibrations of an elastically connected rectangular plate–membrane system. Solutions of the problem are formulated by using the Navier method. Natural frequencies of the system in the form of two infinite sequences are determined. Normal mode shapes of vibration expressing two kinds of vibration, synchronous and asynchronous, are presented. The initial-value problem is also solved. In a numerical example, the effect of membrane tension on the natural frequencies of this mixed system is discussed.