Free vibrations of a rectangular panel backed by a closed rectangular cavity by a closed rectangular cavity

Abstract An exact solution is found for the acoustic velocity potential in a closed box with one flexible wall. The walls of the box, other than the flexible wall, are assumed to be hard (i.e. perfect acoustic reflectors). The results of this analysis are used to find the effect in terms of acoustic stiffnesses of such a backing cavity on panel vibrations. The resulting modifications to in vacuo values of panel natural frequency and mode shape are found for two panel-cavity systems. It is concluded that there are two distinct types of panel-cavity system. In the first type the action of. a closed cavity on panel dynamics is negligible. This type of system is characterized by acoustic stiffnesses which are considerably less than the panel stiffnesses. The second type of system is characterized by acoustic stiffnesses of the same order as or greater than the panel stiffnesses. Considerable modification of panel mode shapes and natural frequencies takes place for this class of system. For this second system it is concluded that the effect of the cavity must be taken into account in the analysis of any functions dependent upon panel response, such as panel stress or noise transmission. An outline is given of the limitations and further applications of this work.