分层结构中兰姆波二次谐波发生的模式展开分析  

Modal expansion analyses of second-harmonic generation of the Lamb waves in layered structures

作　　者：邓明晰 

机构地区：[1]后勤工程学院物理教研室,重庆400016

出　　处：《声学学报》2005年第2期132-142,共11页Acta Acustica

基　　金：国家自然科学基金资助项目(10004016)

摘　　要：采用二阶微扰近似和模式展开方法,对分层结构中兰姆波的二次谐波发生问题进行了深入研究,得到了二次谐波声场的一般表达式。兰姆波在分层结构中传播时,固体板材的体弹性非线性效应导致在各固体层的内部及表面出现二倍频的体驱动力及面驱动应力,其作用是在分层结构中激发出一系列二倍频兰姆波的简正模式,这些简正模式的叠加即构成分层结构中兰姆波的二次谐波声场。当构成二次谐波声场的某一二倍频兰姆波简正模式的相速度等于基频兰姆波的相速度时,该二倍频兰姆波简正模式分量表现出随传播距离积累增长的性质。本文还就铝板-环氧粘接层-铝板结构中兰姆波的二次谐波声场进行了数值分析,结果显示,软粘接层性质对二次谐波声场的影响很大。Through second-order perturbation approximation and modal expansion approach, the second-harmonic generation of a primary Lamb wave propagating in layered structures has been analyzed, and the general solution to second-harmonic displacement fields has been obtained. Because of the bulk elastic nonlinearities of solids, there are double frequency bulk driving forces in the interior of each layer and double frequency traction stress tensors at the two surfaces of each layer when a primary Lamb wave travels along layered structures. These driving forces and traction stress tensors of double the primary frequency generate a series of double frequency Lamb wave normal modes (abbr. DFLMs), and the summation of a series of DFLMs constitutes the second-harmonic fields of a primary Lamb wave. It is found that the DFLM component of a primary Lamb wave can grow with propagation distance down layered structures when its phase velocity equals that of a primary Lamb wave. Numerical simulations of second-harmonic displacement fields of a primary Lamb wave have been carried out for a layered structure consisting of aluminum-epoxy-aluminum. The results show that the properties of soft adhesive joint play a dominant role in generation of the second harmonics.

关 键 词：二次谐波发生 分层结构 兰姆波 模式展开 简正模式 一般表达式 非线性效应 二倍频 展开方法 微扰近似 传播距离 数值分析 相速度 粘接层 声场 动应力 驱动力 板结构 固体 性质 二阶 表面 弹性 

分 类 号：O422.2[理学—声学]