Natural Vibration of a Cavity Backed Rectangular Plate Using A Receptor-Rejector System Model

Forced vibration of a cavity backed rectangular plate is widely used to study the physics of noise transmission into an enclosure. In this context, the cavity backed plate is a dynamical system with coupled motion of the plate and the air cavity. The natural frequencies of the coupled system are the most important characteristics of the noise transmission into the cavity. This paper investigates the natural vibration of a cavity backed rectangular plate and presents numerical results for the particular case of a cavity backed simply supported plate. The natural vibration of the total system is viewed as the result of the interactions of various natural modes of vibration of its subsystems. The physics of the modal interactions is discussed using a receptor-rejector system model, and the dynamics of the cavity backed panel is investigated using the plate receptance and the cavity rejectance (inverse receptance) parameters. The modal interactions are further clarified using a cavity backed piston forming a single degree of freedom system. With the principle of superposition, the receptor-rejector system model can be used to analyze cavities with more than one flexible wall.