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Nonlinear Travelling Waves in a Neo-Hookean Plate Subjected to a Simple Shear

Propagation of nonlinear travelling waves in a neo-Hookean plate subjected to a plane-strain simple shear is considered in this paper as a model problem for waves propagating along nonprincipal directions of stretch. The evolution equation for a monochromatic wave is derived with the aid of the virtual work method. We show that the coefficient of the nonlinear term in the evolution equation is real and that this is also true for general form of the strain energy function and prestress. Thus nonlinear travelling waves with constant amplitude and amplitude dependent velocity can propagate in such a prestressed plate. The effect of shear strain on the stability of such nonlinear travelling waves with respect to side-band perturbations is also studied. It is shown that a simple shear has a destabilizing effect.