层状压电结构中超声导波的非线性效应研究

It is of significance in theory and application to perform the theoretical and experimental studies of nonlinear effects of ultrasonic guided waves propagating in layered piezoelectric structures. Under the condition that the mechanical-electrical coupling is taken into account, in the present project, the modal expansion equation of the second harmonic of ultrasonic guided wave propagation in layered piezoelectric structures will be established, and its analytical solution will be presented, based on the in-depth studies of the nonlinear constitutive relationships of stress and electrical displacement in piezoelectric materials. The interaction relationship of the nonlinearities of elasticity, piezoelectricity and dielectricity to the effect of second-harmonic generation of ultrasonic guided wave propagation will be investigated theoretically. The influence of the complicated anisotropy of layered piezoelectric structures as well as the guided wave dispersion on the effect of second-harmonic generation will be studied theoretically and experimentally. Moreover, the internal relationship of the mechanical and electrical boundary conditions to the effect of second-harmonic generation of ultrasonic guided wave propagation will be investigated theoretically and experimentally. Whereafter, an approach or means of regulating the efficiency of second-harmonic generation of ultrasonic guided waves in layered piezoelectric structures will be examined through changing the electrical boundary condition at each surface/interface. Through the studies of the present project, an in-depth insight into the physical process of second-harmonic generation of ultrasonic guided waves, as well as its propagation characteristic, will be obtained under the condition that the mechanical-electrical coupling is taken into account. Further, the internal relationship of the multi-nonlinearities and complicated anisotropy of layered piezoelectric structures, as well as the mechanical in particular electrical boundary condition at each surface/interface, to the effect of second-harmonic generation of ultrasonic guided waves can be understood deeply. There is no doubt that the studies in the present project will lay a theoretical and experimental foundation for practical applications.

开展层状压电结构中超声导波非线性效应的理论和实验研究具有重要的理论和实际意义。本项目在深入研究力-电耦合条件下应力及电位移矢量的非线性本构关系的基础上，建立层状压电结构中超声导波二次谐波的模式展开方程并给出其解析解。理论上深入研究弹性、压电和介电等非线性与超声导波二次谐波发生效应之间的相互作用关系，理论和实验上深入研究层状压电结构复杂的各向异性和导波的色散特性对二次谐波发生效应所产生的影响，以及力学和电学边界条件与二次谐波发生效应的内在联系，并探索一种以改变界面或表面电学边界条件的方式调控超声导波二次谐波发生效率的方法或途径。通过本项目的立项研究，可深刻理解与把握力-电耦合条件下超声导波二次谐波发生效应的物理过程及其传播规律，可深入了解层状压电结构的多种非线性、复杂的各向异性以及力学尤其是电学边界条件等因素与超声导波二次谐波发生效应之间的内在联系，进而为相关的应用研究奠定理论和实验基础。

开展层状压电结构中超声导波非线性效应的理论和实验研究具有重要的理论和实际意义。本项目在深入研究力-电耦合条件下应力及电位移矢量的非线性本构关系的基础上，建立了层状压电结构中超声导波二次谐波的模式展开方程，并给出了相应的二次谐波声场之解析解。从理论上深入研究了弹性、压电和介电等非线性与超声导波二次谐波发生效应之间的相互作用关系，深入分析了层状压电结构复杂的各向异性和导波的频散特性对二次谐波发生效应所产生的影响，以及力学和电学边界条件与二次谐波发生效应的内在联系，探索了一种以改变界面/表面电学边界条件的方式调控超声导波二次谐波发生效率的方法。借助于本项目的研究结果，可深刻理解与把握力-电耦合条件下超声导波二次谐波发生效应的物理过程及其传播规律，可揭示出弹性非线性、压电非线性和介电非线性等在超声导波二次谐波发生过程中的相互作用关系，可厘清各向异性、力学电学边界条件(尤其是电学边界条件)等因素与超声导波二次谐波发生效应之间的内在联系，为复杂结构中超声导波的理论及应用研究工作的开展奠定了基础。此外，在本项目的支持或部分支持下，基于所建立的非线性超声导波实验测量系统，进一步实验研究了采用非线性超声(超声导波)方法评价材料早期损伤的可行性，实验研究了以非线性超声导波方法评价固体板材表面/界面性质的可行性，研究了非线性周向超声导波的传播特性，以及研究了单一超声导波模式的激励方法，等等。