Generation of cumulative sum frequency acoustic waves of shear horizontal modes in a solid plate

Abstract

The physical process of generation of the cumulative sum frequency acoustic waves (SFAWs) of shear horizontal (SH) modes propagating in a solid plate is described in this paper. Due to the bulk elastic nonlinearity of material of the solid plate, there will be the SFAWs and difference frequency acoustic waves (DFAWs) once an excitation source of SH modes include two or more frequencies. A technique based on second-order perturbation is given for analyzing generation of the SFAWs and DFAWs, which arise from the nonlinear cross interaction of the partial shear waves of SH modes with the different frequencies. The following conclusions have been acquired in this paper. The DFAWs must not have a cumulative growth effect, the SFAWs may have a cumulative growth effect once some conditions are satisfied, and the SFAW fields with cumulative growth effect may be symmetrical or antisymmetrical. This paper also derives the analytical solution of the cumulative SFAWs, which satisfies the boundary and initial conditions of excitation. Numerical results clearly reveal the distortion and growth effects of the cumulative SFAW field patterns along the propagation direction, as well as the dependence of the cumulative SFAW field patterns on the position of the excitation source. The process of analysis shown in this paper yields clear physical insight into the cumulative SFAW generation of SH modes with different frequencies not previously available.