Abstract
It is shown that there are four conserved properties of an elastic wave in an infinite isotropic plate: the energy, the two components of wave momentum parallel to the surface, and wave angular momentum normal to the surface. All four invariants are volume integrals of quadratic functions of the spatial (Eulerian) coordinates. The canonical energy-momentum density tensor and the orbital, spin, and total angular momentum density tensors are constructed and sufficient conditions for their conservation are demonstrated. A procedure for measuring the wave momentum of a surface wave is proposed. It is argued that these invariants are likely to be particularly useful characterizations of acoustic emission, e.g., from a growing crack. Experimental tests are proposed, and possible applications to practical monitoring problems described.
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