圆管结构中的非线性周向导波*

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。

Nonlinear circumferential guided waves propagating in a circular tube

On the basis of a second-order perturbation approximation and a modal expansion analysis approach, the relevant problems of nonlinear circumferential guided wave (CGW) propagation in a circular tube can effectively be solved in theory. According to the results of numerical calculations and finite element simulations, 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 where the selected mode pair of primary and double frequency CGWs simultaneously 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.