波导结构中的衰逝波特性研究

In the waveguides, the boundary and the wave field near the defect and load represent a diverse superposition of guided propagating waves, guided evanescent waves with exponential attenuation and guided evanescent waves with damped attenuation. Investigating guided evanescent waves is necessary to exactly understanding the complicated interactions between guided wave and defects, and is the base of evaluating the shape and size of defects. This project will develop an asymptotically analytical approach, which is based on the orthogonal polynomial technique, to solve the guided evanescent waves in anisotropic structures, multilayered structures and functionally graded structures. The 3D dispersion curves describing wave speed、attenuation and frequency will be obtained. The displacement distribution will also be calculated. Secondly, the proposed approach will be introduced into cylindrical coordinates so that the guided evanescent waves in various hollow cylinders can be solved. The influences of elastic constant, stacking sequence and thickness, gradient index of the graded structure will be investigated. Simultaneously, this approach will be introduced into waveguides composed of piezoelectric material and magneto-electric-elastic material in order to solve their 3D dispersion curves, stress and electric potential distributions. The influences of coupled fields will be investigated. The guided evanescent mode with higher wave speed, lower attenuation and higher electromechanical coupling coefficient will be found to guide the design and optimization of the transducers using guided evanescent mode, which would have higher resolution and energy conversion efficiency. Finally, the excitation of single guided evanescent mode would be investigated so that the finite element simulations and guided wave propagation experiments could be implemented to verify the correctness of the proposed approach.

在波导的边界，负载和缺陷附近的波场中同时存在传播波、指数衰减的衰逝波和阻尼衰减的衰逝波。研究衰逝导波是准确理解导波与缺陷之间复杂关系的基础，也是实现缺陷形状和尺寸精确导波无损检测的基础。本项目将开发一种基于正交多项式技术的渐近解析计算方法，以求解各向异性结构、多层结构、功能梯度结构中的衰逝导波，得到描述波速、衰减和频率的三维频散曲线，揭示弹性常数、叠层顺序与材料梯度变化形式等对衰逝导波的影响。然后将该方法引入圆柱坐标系中，研究圆柱形波导结构中的衰逝波，并进一步将该方法推广到压电、磁-电-弹等多场耦合结构，研究其衰逝导波频散特性和应力、电势、磁势分布特征，揭示耦合作用对衰逝导波特性的影响；寻找结构中波速快、衰减低而机电耦合系数高的衰逝导波模态，指导基于衰逝导波换能器的设计与优化，提高其分辨率和能量转换效率。最后，研究单一衰逝导波模态的激励，通过有限元模拟和衰逝导波实验验证计算方法的正确性。

在波导的边界，负载和缺陷附近的波场中同时存在传播波、指数衰减的衰逝波和阻尼衰减的衰逝波。研究衰逝导波是准确理解导波与缺陷之间复杂关系的基础，也是实现缺陷形状和尺寸精确导波无损检测的基础。本项目开发了一种基于正交多项式技术的渐近解析计算方法，应用提出方法研究了各向异性板、功能梯度板等结构中的衰逝导波；研究表明：SH衰逝波只有纯虚波数模态，Lamb衰逝波有纯虚波数模态和复波数模态；SH衰逝波各阶模态起始于零频，终止于某截止频率处。对于Lamb衰逝波纯虚数分支，低频处模态是起始某截止频率处，而终止于相邻截止频率处；对于复数分支，低频处模态总是起始于零频，终止于纯实数或纯虚数分支的极值处。纯虚波数衰逝波呈指数形式衰减但并不随距离传播；复波数衰逝波呈阻尼正弦式衰减，当虚部波数很小时可以传播很远的距离；当频率增加到一定值时，会发生波模态由衰逝波转变为传播波。其次，将该方法引入柱坐标系和球形坐标系中，研究了功能梯度柱形和球形曲面波导结构中的传播波和衰逝波特性；研究表明：径厚比和梯度场对衰逝导波频散有显著影响；随着径厚比的增大，衰逝波衰减得更快；不同梯度场的材料体积含量不同，衰逝波频散特性不同。接着，进一步将该方法推广到压电、磁-电-弹等多场耦合结构，研究其衰逝导波频散特性和应力、电势、磁势分布特征；寻找结构中波速快、衰减低而机电耦合系数高的衰逝导波模态，指导基于衰逝导波换能器的设计与优化，提高其分辨率和能量转换效率；研究表明：高频处存在一些衰减很小但波速高的复波数模态；材料的压电性和力学与电学边界条件对导波复频散特性都有较大影响；力学自由边界条件下，电学边界条件对衰逝波频散影响显著；而力学固定边界条件下，电学边界条件对衰逝波频散影响很小。最后，通过有限元模拟和导波实验验证了提出方法的正确性。