SIMPLE-MODELS OF ENERGY-FLOW IN VIBRATING MEMBRANES

A simplified model of the energy distribution and energy flow in membr anes is derived using a loss factor damping model, an energy balance a nd a simplified energy transmission relationship. The energy transmiss ion relationship is derived by smoothing a generalized plane wave repr esentation of the energy density and intensity in the membrane. For sm oothed conditions, the intensity is proportional to the spatial deriva tives of the energy density. The resulting energy model is a second or der differential equation which predicts the smoothed energy distribut ion and intensity in a membrane. The capabilities of the model are ill ustrated for four cases of broadband excitation of a point excited mem brane.