Investigating acoustoelasticity of plane elastic waves and second harmonics within isotropic solid media: A novel approach

Abstract

This paper presents a novel approach to investigating the acoustoelasticity of plane elastic waves and second harmonics within isotropic solid media. The new contributions of this approach consist of providing an intuitive understanding of the essence of acoustoelasticity, offering a more straightforward method to deduce the expressions for acoustic velocities and pre-strains in natural coordinates compared to conventional theory of acoustoelasticity, and introducing a novel methodology for investigating acoustoelasticity of plane elastic waves and second harmonics. The core idea of this approach can be explained as follows: by introducing an intermediate state for describing predeformation between the natural state and the final state, the predefomation can be integrated into the nonlinear wave equation, and acoustoelastic equations of plane elastic waves and second harmonics can be deduced consequently by decomposing this nonlinear wave equation under the second approximation of perturbation theory. When applying this approach to study the acoustoelasticity of P wave and S wave of plane elastic waves, the validity and practicality of this approach are confirmed by contrasting expressions for acoustic velocities and pre-strains in natural coordinates to those found in previous research [8], which exhibit perfect consistency. Furthermore, this paper focuses on the acoustoelasticity of the free second harmonics and the driven second harmonics generated by self-excitation and interaction of plane elastic waves. The results concerning acoustoelasticity can be summarized as follows: firstly, pre-strain only influences wave vectors of plane elastic waves through the speed term in their expressions without altering their amplitudes; secondly, the acoustoelasticity of free second harmonics follows similar rules above; finally, Pre-strain affects the amplitudes and wave vectors of driven second harmonics through the speed terms in their expressions without changing the form of their expressions.