Is power equipartitioned in complicated structures?

Abstract

A tenet of statistical energy analysis is that power of an elastic wave is partitioned equally among the substructures of an overall structure, and prevails when modes of each overlap those of the other substructures. Is power equipartition achieved for all complicated structures, specifically, for those in which several wave types spatially coexist? Recent research equivocates: only sometimes! Analysis by He for a finite-length ringed shell in water shows power equipartition among compressional, shear, and flexural waves. But measurements by Machens and Dyer, and by Bondaryk, on various 3-D truss structures in air, do not show power equipartition. An explanation for the apparent contradiction in these different structural systems is not, at this writing, worked out. Speculations, however, point to the differences between scattering from one wave type to another, on the shell and in the truss. On the shell, scattering at a ring is distributed with finite width in helical angle. In the truss, scattering is localized at truss joints. Both systems have spatial regularity and hence stopbands, but the helical angle width on the shell can induce good wave–wave spatial overlap, while no ‘‘extra’’ dimension is available in the truss to counter the stopband rejections. [Supported by ONR.]