Interesting effects in harmonic generation by plane elastic waves 
期刊名称Acta Mechanica Sinica
作者Yanzheng Wang; Jan D. Achenbach
摘要The harmonics of plane longitudinal and transverse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonlinearity, a transverse wave generates a second longitudinal harmonic. This propagates with the velocity of transverse waves, as well as resonant transverse first and third harmonics due to the cubic and quadratic nonlinearities. A longitudinal wave generates a resonant longitudinal second harmonic, as well as first and third harmonics with amplitudes that increase linearly and quadratically with distance propagated. In a second investigation, incidence from the linear side of a primary wave on an interface between a linear and a nonlinear elastic solid is considered. The incident wave crosses the interface and generates a harmonic with interface conditions that are equilibrated by compensatory waves propagating in two directions away from the interface. The back-propagated compensatory wave provides information on the nonlinear elastic constants of the material behind the interface. It is shown that the amplitudes of the compensatory waves can be increased by mixing two incident longitudinal waves of appropriate frequencies.
关键词Cubic nonlinearity; Third harmonic; Quadratically cumulative behavior; Interface; Compensatory wave
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基金项目The work was supported by the National Natural Science Foundation of China (Grants 11621062 and 11532001) and the China Scholarship Council (CSC).
作者地址1 Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China;
2 Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA

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