SIMPLE-MODELS OF THE ENERGETICS OF TRANSVERSELY VIBRATING PLATES

Approximate energy models for infinite and finite plates are derived using three relationships; an energy balance, a loss factor damping model and an approximate energy transmission model. The energy transmission relationship for the infinite plate relates the far field radial intensity, the group speed and the local energy density. The resulting energy equation for infinite plates is an excellent approximation in the far field. For finite plates, the far field energy density and intensity expressions for plane wave approximations are smoothed in order to derive an energy transmission relationship. The resulting relationship is analogous to Fourier's law of heat conduction. The energy model is a second order equation which models the smoothed far field energy distribution. The equations model the general behavior of finite plates well and explain the dependence of plate energetics on frequency and damping.