各向异性固体板中的非线性超声导波  

Nonlinear ultrasonic guided waves in an anisotropic solid plate

作　　者：邓明晰 

机构地区：[1]后勤工程学院,重庆400016

出　　处：《声学学报》2008年第3期252-261,共10页Acta Acustica

基　　金：国家自然科学基金(10674180);教育部新世纪优秀人才支持计划(NCET-05-X)资助项目

摘　　要：将超声导波的非线性视为线性波动响应的一个二阶微扰,采用二阶微扰近似和导波的模式展开分析方法,从理论上研究了各向异性固体板中超声导波的二次谐波发生效应,给出了超声导波二次谐波声场的一般形式解。板材的各向异性可从多个方面对二次谐波发生效应产生影响,尤其是板材各向异性引起的导波模式相速度的改变,可显著地影响到构成导波二次谐波声场的二倍频导波模式随传播距离的积累增长程度。根据理论分析和数值计算结果可知,在不同传播方向上超声导波的非线性效应存在较显著的差异,伴随基频导波模式的传播所发生的二次谐波对固体板材的各向异性表现出更为敏感的性质,这一结果可为准确定征板材的弹性各向异性提供一种理论依据。The nonlinearity in ultrasonic guided waves was treated as a second-order perturbation of the linear wave motion response. Based on the approaches of second-order perturbation approximation and modal expansion analysis for waveguide excitation, the effect of second-harmonic generation of primary （fundamental） ultrasonic guided wave propagation in an anisotropic solid plate has been studied theoretically. The general formal solution to second-harmonic displacement field of primary ultrasonic guided waves has also been presented. It was found that the elastic anisotropy of the plate material might, in several aspects, influence the effect of second-harmonic generation of guided wave modes. Especially, the changes in the phase velocities of guided waves, caused by the elastic anisotropy of the plate material, might clearly influence the degree of accumulative growth of double frequency guided wave modes, constituting the field of second harmonic of primary guided waves, with propagation distance. In terms of the results of theoretical analyses and numerical calculations, it was known that there was obvious difference in the nonlinear effect of ultrasonic guided waves in different directions of propagation, and that the second harmonic of primary guided wave propagation was highly sensitive to the elastic anisotropy of the plate material. The results obtained might provide a theoretical basis for accurate characterization of the elastic anisotropy of the plate material by using the nonlinear effect of ultrasonic guided wave propagation.

关 键 词：弹性各向异性 非线性效应 超声导波 固体板 二次谐波 导波模式 微扰近似 传播距离 

分 类 号：O426[理学—声学]