Evolution equation for nonlinear Scholte waves

摘要

The evolution equations for nonlinear Scholte waves (finitenamplitude elastic waves propagating along liquid/solid interface), whichnaccount for the second order nonlinearity of a liquid, are derived fornthe first time. For mathematical simplicity the nonlinearity of thensolid, which influence is expected to be weak in the case of weaknlocalization of the Scholte wave, is not taken into consideration. Thenanalysis of these equations demonstrates that the nonlinear processesncontributing to the evolution of the Scholte wave can be divided intontwo groups. The first group includes nonlinear processes leading to wavenspectrum broadening which are common to bulk pressure waves in liquidsnand gases. The second group includes the nonlinear processes which arenactive only in the frequency down-conversion (leading to wave spectrumnconservation or narrowing), which are specific to the confined nature ofnthe interface wave. It is demonstrated that the nonlinear parameters,nwhich characterize the efficiency of various nonlinear processes in theninterface wave, strongly depend on the relative properties of thencontacting liquid and solid (or, in other words, on the deviation of thenScholte wave velocity from the velocities of sound in liquid and innsolid). In particular, the sign of the nonlinear parameter responsiblenfor the second harmonic generation can differ from the sign of thennonlinear acoustic parameter of the liquid. It is also verified thatnthere are particular liquid/solid combinations where the nonlinearnprocesses, which are inactive in the frequency up-conversion, dominatenin the evolution of the Scholte wave. In this case distortionlessnpropagation of the finite amplitude harmonic interface wave is possible.nThe proposed theory should find applications in nonlinear acoustics,ngeophysics, and nondestructive testing