Interesting effects in harmonic generation by plane elastic waves

作     者：Yanzheng Wang Jan D.Achenbach 

作者机构：Department of Engineering Mechanics Zhejiang University Department of Mechanical Engineering Northwestern University 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2017年第33卷第4期

页      面：754-762页

核心收录：

学科分类：08[工学] 080102[工学-固体力学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China (Grants 11621062 and 11532001) the China Scholarship Council (CSC) 

主　　题：harmonic longitudinal resonant transverse nonlinearity cubic incident solids propagating constants 

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 *** 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.