功能梯度圆柱板中的周向衰逝导波

Circumferential Evanescent Guided Waves in Functionally Graded Cylindrical Curved Plates

与传播波模态不同,衰逝波模态波数为纯虚数或复数,它们随传播距离呈指数或阻尼式衰减.具有复波数的衰逝波对结构缺陷形状和尺寸的导波检测具有重要作用,但其求解却是非常困难的,通常要借助于各种迭代技术.论文提出一种计算求解衰逝波问题的改进的Legendre正交多项式方法,该方法可将复杂的变系数微分方程组计算转换为特征值求解问题,无需迭代便能计算得到包含实波数域、虚波数域和复波数域的完整的频散曲线.通过具体算例验证了提出方法的正确性.应用提出方法计算了不同梯度圆柱板中的衰逝导波,绘制了三维频散曲线,研究了不同径厚比和梯度场对衰逝导波频散的影响,分析了衰逝导波的位移和应力分布,讨论了衰逝导波的传播特性.

Evanescent wave modes are substantially different from the propagating modes,which are associated with non-real wavenumbers and decay exponentially or damp with propagation distance.Such modes with complex wavenumbers play an important role in the detection of the shape and size of defects.However,it is very difficult to obtain the complex solutions of the dispersion equation corresponding to the evanescent waves,especially for demanding cases,such as those involving composite materials and curved structures.In this study,an improved orthogonal polynomial method is proposed to deal with the problems of evanescent guided waves in a functionally graded cylindrical curved plate.The proposed method can convert the complex differential equations with variable coefficients into an eigenvalue problem and obtain all the purely real,purely imaginary and complex solutions without iterative process.The validity of the proposed method is illustrated by specific numerical examples.Three dimensional full-dispersion curves of the guided waves in various graded cylindrical curved plates are obtained,and the effects of different radiusthickness ratios and graded fields on the dispersion characteristics of guided evanescent waves are illustrated.The displacement amplitude and stress distributions are also discussed to analyze the specificities of the evanescent guided waves.Numerical results show that there are only purely real and purely imaginary branches for circumferential shear horizontal（SH）waves;but for circumferential Lamb-like waves,there are purely real,purely imaginary and complex branches.Most complex branches collapse onto the minima of purely imaginary branches and local inflection points,and occasionally appear on higher-order real branches.The complex branches exhibit both local vibration and local propagation,which turn into real branches with increasing frequency.Both the radius-thickness ratio and the graded field have significant effects on dispersion curves.With the increase of radius-thickness ratio,the decay of evanescent waves is faster.All the results presented in this work can provide theoretical guidance for ultrasonic nondestructive evaluation.