NONLINEAR TRAVELING WAVES IN A NEO-HOOKEAN PLATE SUBJECTED TO A SIMPLE SHEAR

Propagation of nonlinear travelling waves in a neo-Hookean plate subje cted to a plane-strain simple shear is considered in this paper as a m odel problem for waves propagating along nonprincipal directions of st retch. The evolution equation for a monochromatic wave is derived with the aid of the virtual work method. We show that the coefficient of t he nonlinear term in the evolution equation is real and that this is a lso 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 eff ect of shear strain on the stability of such nonlinear travelling wave s with respect to side-band perturbations is also studied. It is shown that a simple shear has a destabilizing effect.