Conserved quantity of elastic waves in multi-layered media: 2D SH case — Normalized Energy Density

Abstract

We introduce a new conserved quantity, Normalized Energy Density (NED), alternative to the conventional definition of energy for a layered structure in a 2D SH problem. NED is defined by the average of power of a half transfer function multiplied by the impedance, and the conservation across the material interface is analytically proved for a two-layered case. For three, four, and ten-layered cases, the conservation is examined by applying the Monte Carlo simulation method, and then NED is supposed to be conserved through the layers.