Energetics of vibrating systems

This investigation explores the use of energy variables to predict the response of vibrating structures subject to broadband and narrowband high frequency excitations. The structures considered in this investigation are thin plates, membranes, and acoustic enclosures. Governing equations for the smoothed distribution of the energy density in these subsystems are derived, verified and implemented using the Finite Element Method. The derivation of the energy governing equations is based on fundamentals from continuum mechanics. An energy transmission relationship which relates the energy density to the flux of energy is derived for each subsystem. An energy balance and a power dissipation relationship are then used in conjunction with the transmission relationship to derive the energy governing equation. Although the response prediction obtained from the smoothed energy density is approximate, it is representative of the global behavior of the structure in question. The energy governing equations are formulated using the Finite Element Method. The FEM formulation of the energy governing equations is used to obtain vibrational energy predictions of problems with complex geometries and uneven damping distribution. The FEM formulation of the energy equation is also used as a design tool to make parameter studies of a certain design. This investigation considers the total variation of the energy density in vibrating beams. A spatially harmonic component of the energy density and a nearfield component can be used in conjunction with the smooth components of the energy density to make more detailed narrowband predictions of the energy density in vibrating beams. The method used to formulate the energy density and power boundary conditions is demonstrated. All the results obtained in this investigation are verified by comparisons with predictions obtained via classical schemes