Energy source identification using reactive structural intensity

Abstract

The analysis of wave propagation phenomena in structures, especially energy flux, can be a powerful approach to noise and vibration control problems. The active mechanical intensity corresponds to the period-averaged value and is related to the propagative wave field. The reactive intensity is related to the reverberance of energy in the structure, which originates the standing waves or mode shapes. Properly separated into its wave components, reactive intensity maps agree well with operational modes, indicating the location of the nodal lines. On the other hand, active intensity is the quantity usually addressed when solving vibration and noise problems, since it provides information about the main energy flow paths, thus enabling identification of the energy sources and sinks. For highly reverberant structures, however, measuring active intensity becomes awkward, and intensity plots fail to indicate the region where the energy is injected or dissipated in the structure. A new technique to localize energy sources based on the divergence of the reactive intensity and the distribution of the potential and kinetic energy densities within the structure is presented. Numerical results are given for a beam with a point excitation using finite-element and spectral element models based on the Bernoulli–Euler beam theory.