Abstract
In isotropic solids, transverse acoustic waves propagate undistorted and the interaction of collinear transverse waves is forbidden. In this study, It is found that transverse and longitude waves behave differently in anisotropic solids and the different formulas are given for the interaction of transverse and longitude acoustic waves propagating in different kinds of crystals including cubic, trigonal, tetragonal, hexagonal crystals. The formulas are expressed in terms of the derivatives of the strain energy. The formulas are used to calculate the interaction coefficients in the general anisotropic medium emphasizing the influence of nonlinearities. The evolution equations are derived for the wave amplitudes and find analytical formulas for all interaction coefficients of quadratically nonlinear interacting waves. The equations of motion show that transverse and longitude waves are distort as they propagate and interact. It is observed that two acoustic waves with frequency can produce harmonic waves with sum and difference frequency. This shows evidence that the intrinsic nonlinearities of an anisotropic solid can induce an interaction of acoustic waves. This project is supported the National Basic Research Program of China (Grant Nos. 2012CB921504, 2011CB707902), financial support of the National Natural Science Foundation of China (Grant No. 11074122), fundamental Research Funds for the Central Universities (Grant Nos. 1113020403, 1101020402), State Key Laboratory of Acoustics, Chinese Academy of China (Grant No. SKLOA201005) and A project funded by the priority academic program development of Jiangsu higher education institutions.
Published Version
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