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Resonant interactions of nonlinear transverse waves in incompressible magnetoelasticity

Domański W.

Journal of Technical Physics

1999

Vol. 40, no 4

435-446

The asymptotic expansion of high-frequency small-amplitude waves is applied to the equations of a nonlinear, elastic, incompressible solid interacting with a magnetic field. The single space dimension case is discussed. The evolution transport equations of weakly nonlinear geometric optics for the interacting nonlinear magnetoelastic waves are derived. In contrast to the zero background field, the nonzero prestrain initial data (around which the asymptotics is applied) imply that some of the resonant interacting coefficients are nonzero. All such coefficients are calculated explicitly and analysed for a certain nonzero constant state. Finally the equations for resonant triads are displayed.