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第 37 卷 第 5 期                                                                        Vol. 37, No.5
             2018 年 9 月                          Journal of Applied Acoustics                 September, 2018

             纪念应崇福院士诞辰100周年




                               圆管结构中的非线性周向导波                                            ∗





                                          高广健     1    李明亮      1   邓明晰      1,2†


                                                 (1 陆军勤务学院     重庆   401331)
                                                   (2 重庆大学   重庆   400044)

                摘要    采用将二阶微扰近似与模式展开分析相结合的方法，可从理论上有效求解圆管结构中的非线性周向导
                波问题。通过数值计算和有限元仿真发现，基频与二倍频周向导波模式的相速度匹配程度，可显著影响二倍频
                周向导波模式随传播周向角的积累增长程度。针对基频与二倍频周向导波模式的相速度和群速度均相匹配的
                情形，通过实验研究发现，周向导波确可存在强烈的非线性效应，且周向导波的二次谐波发生效应可对圆管早
                期损伤状态做出敏感的响应。文中给出的有关结果，可为进一步开展非线性周向导波的研究工作奠定理论和
                实验基础。
                关键词     周向导波，二次谐波发生，模式展开分析，积累效应，损伤评价
                中图法分类号: O426.2          文献标识码: A          文章编号: 1000-310X(2018)05-0680-11
                DOI: 10.11684/j.issn.1000-310X.2018.05.012





                   Nonlinear circumferential guided waves propagating in a circular tube



                                    GAO Guangjian  1   LI Mingliang 1  DENG Mingxi 1,2

                                     (1 Army Logistics University of PLA, Chongqing 401331, China)
                                         (2 Chongqing University, Chongqing 400044, China)

                 Abstract  On the basis of a second-order perturbation approximation and a modal expansion analysis ap-
                 proach, the relevant problems of nonlinear circumferential guided wave (CGW) propagation in a circular tube
                 can be effectively solved in theory. According to the results of numerical calculations and finite element sim-
                 ulations, it is found that the degree of phase velocity matching between the primary and double frequency
                 CGW modes can significantly affect the effect of cumulative growth of the double frequency CGW mode with
                 circumferential angle. For the case which the selected mode pair of primary and double frequency CGWs simul-
                 taneously satisfies both the phase and group velocity matching, the experimental investigations show that the
                 CGW mode does have a strong nonlinear effect, and that the effect of second harmonic generation of primary
                 CGW propagation is sensitive to the early damage state of the circular tube. The results presented here lay a
                 theoretical and experimental foundation for further investigations on nonlinear CGWs.
                 Key words Circumferential guided wave, Second-harmonic generation, Modal expansion analysis, Cumula-
                 tive growth effect, Evaluation of damage

             2018-06-13 收稿; 2018-08-02 定稿
             国家自然科学基金项目 (11474361, 11704410)
             ∗
             作者简介: 高广健 (1985- ), 男, 黑龙江宁安人, 博士, 讲师, 研究方向: 超声检测。
             † 通讯作者 E-mail: dengmx65@yahoo.com
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