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第 41 卷 第 5 期                                                                       Vol. 41, No. 5
             2022 年 9 月                          Journal of Applied Acoustics                 September, 2022

             ⋄ 研究报告 ⋄



                     非线性兰姆波在厚度缓慢变化和衰减下的


                                                   特性分析             ∗





                                         左炜翌      1,2  安志武      1,2†  张碧星     1,2


                                    (1  中国科学院声学研究所      声场声信息国家重点实验室         北京  100190)
                                                (2 中国科学院大学      北京  100190)

                摘要：该文运用解析的方式推导了考虑声波衰减时兰姆波二次谐波的累积和传播规律，并用半解析方式将该
                理论推广到缓慢变厚度板的情况。由于色散特性，兰姆波二次谐波和基频波相速度不匹配，传播通常会产生拍
                频效应，使得二次谐波的振幅沿着传播距离周期性的归零。当考虑声波衰减或板的厚度缓慢变化的情况时，拍
                频效应将不再严格地被满足。二次谐波的振幅依然会沿着传播距离而振荡，但不会归零。该研究可以用于分
                析如何高效地激发和接收兰姆波的二次谐波，表征和评估不同厚度变化的结构中的微观结构损伤。
                关键词：非线性兰姆波；衰减；变厚度；二次谐波
                中图法分类号: O426.2          文献标识码: A          文章编号: 1000-310X(2022)05-0721-06
                DOI: 10.11684/j.issn.1000-310X.2022.05.005



                 Characteristics of nonlinear Lamb waves with slowly-varying thickness and

                                                      attenuation


                                      ZUO Weiyi  1,2  AN Zhiwu 1,2  ZHANG Bixing 1,2


                  (1  State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China)
                                   (2  University of Chinese Academy of Sciences, Beijing 100190, China)

                 Abstract: In this paper, the accumulation and propagation of the second harmonics of Lamb waves under
                 attenuation are derived analytically, and the theory is extended to the case of plates with slowly-varying
                 thickness by semi-analytical method. Due to the dispersion characteristics, the phase velocity of the second
                 harmonic wave and the fundamental wave do not match, and the propagation usually produces beat effect,
                 making the amplitude of the second harmonic wave periodically zero along the propagation distance. The beat
                 effect is no longer strictly satisfied when the acoustic attenuation or the slow change in the thickness of the
                 plate are considered. The amplitudes of the second harmonic wave will still oscillate along the distance, but
                 will not return to zero. This study can be used to analyze the conditions for efficient excitation and reception
                 of Lamb wave second harmonics, and to characterize and evaluate microstructure damage in structures with
                 different thickness variations.
                 Keywords: Nonlinear Lamb waves; Attenuation; Variable thickness; Second harmonics


             2021-08-25 收稿; 2021-10-11 定稿
             国家自然科学基金项目 (11874386)
             ∗
             作者简介: 左炜翌 (1996– ), 男, 四川攀枝花人, 博士研究生, 研究方向: 声学。
              通信作者 E-mail: anzhiwu@mail.ioa.ac.cn
             †
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