Propagation and interaction of weakly nonlinear elastic plane waves in a cubic crystal

Abstract

Using the asymptotic method of weakly nonlinear acoustics we analyze the propagation and interaction of elastic plane waves in a cubic crystal. We study the case of an arbitrary direction in a cube face (0 0 1) as well as three selected directions in particular the direction along the cube diagonal which is the threefold symmetric axis of a crystal. In the latter case new evolution equations derived in [W. Domański, Asymptotic equations for weakly nonlinear elastic waves in a cubic crystal, Int. Ser. Num. Math. 129 (1999) 233–241; W. Domański, Weakly nonlinear elastic plane waves in a cubic crystal, Contemp. Math. 255 (2000) 45–61] are recalled. These equations (called complex Burgers equations) describe a quadratically nonlinear interaction of collinear shear and quasi-shear elastic waves in a cubic crystal. Tables of interaction coefficients are displayed in the case of an arbitrary direction in a cube face (0 0 1) revealing possible quadratically nonlinear interactions between all waves in that case.