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

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.

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► Normalized Energy Density (NED) is defined for a layered structure in 2D SH problem.
► Conservation of NED is analytically proved for a two-layered case.
► The conservation is numerically examined for the multi-layered cases.