Wave numbers presented by local energy variables: a limitation for multi-dimensional energy models

摘要

Local energy variables result of the product of two quantities among displacement, strain or stress. In this sense, they are quadratic variables. In time-harmonic wave fields, the timeaveraged energy variables, like structural intensity and energy densities, then present different wave vectors, each resulting from a combination of the two wave vectors of the composing variables (displacement, strain or stress). One dimensional wave systems then present rather simple energy fields: only one wave number is implied for a single propagating plane wave, at most four wave components are present for quadratic variables in the case of forward and backward acoustic plane waves, and these wave numbers only depend on the physical properties of the material. Due to this simplicity, an exact energy formulation is available for one-dimensional energy models. But in two- or three-dimensional systems the energy variables present more complex wave vectors, depending also on geometrical parameters like the relative angle of incidence in the case of two interfering plane waves. This additional complexity is illustrated for energy variables, and its effects for the development of local energy models in multidimensional systems are presented.