考虑表界面效应和尺度效应微纳米磁电结构的振动特性研究

This project aims on the dynamic analsysi of micro/nano laminated magnetoelectric composite strucutre under dynamic mechanical,electric and magnetic loading and the combination of them when synthetically considering the surface elastic effect,surface piezoelectric/piezomagnetic effect,flexoelectric/ flexomagnetic effect and weak interface bonding of the structure. Firstly, a multiphysical constituve model of the laminated magnetoelectric composite is to be elstablished when taking into considering of the surface/interface effect,flexoelectric/flexomagnetic and weak interface bonding. Then the dynamic model of the laminated magnetoelectric composite structure is to be built by the Hamilton variation method, consisting of motion equation of the laminated structure and the equations regarding of the magnetoelectric field as well as the non-classical boundary conditions and the connetive conditions on the interface. By devoloping some feasible numerical methods to solve this whole problem, the magnetoelectric transformation and vibration properties of the micro/nano laminated magnetoelectric structure are obtained and the effects of the surface/interface effect, size effect and weak interface bonding on the dynamic properties of the structures are analyzed. Finally, some experiments are carried out to verify and modify the constitutive model and dynamic analytical model established in this project as well as the numerical methods developed in this project. The work to be conducted in this project is not only of significance on developing the dynamic analysis of the micro/nano structure, but also on providing a theoretical basement for designment and optimization of micro/nano lamianted magnetoelectric composite structure, which shows significant value on the theoretical development and engineering application.

本项目以力、电、磁及其耦合动态载荷作用下微纳米磁电层合材料结构为研究对象，首先综合考虑表面弹性、表面压电/压磁效应、弯电/弯磁效应以及界面弱化等特性，建立微纳米磁电层合材料的力电磁耦合本构模型；通过哈密顿变分原理得到微纳米磁电层合材料结构的动力学控制方程和电磁方程组，以及由于考虑表/界面效应后的非经典边界条件和界面连接条件，由此建立结构的动力学分析模型；通过发展有效的数值计算方法，求解力、电、磁及其耦合动态载荷作用下，微纳米磁电层合材料结构的磁电耦合效应、自由振动和受迫振动以及磁/电响应等特性，分析表/界面效应、尺寸效应以及界面弱化等对结构振动特性和磁电响应的影响，据此对其进行优化设计；通过实验测试验证和修正本项目建立的耦合本构模型和动力学分析模型。本项目的工作将丰富和发展微纳米结构动力学，为微纳米磁电材料及其结构的优化设计，可靠性评定提供理论依据，具有较大的理论意义和工程应用价值。

本项目以力、电、磁及其耦合动态载荷作用下微纳米磁电层合材料结构为研究对象，首先综合考虑弯电/弯磁效应以及界面弱化等特性，建立微纳米磁电层合材料的力电磁耦合本构模型；然后通过哈密顿变分原理得到微纳米磁电层合材料结构的动力学控制方程和电磁方程组，由此建立结构的动力学分析模型；然后通过发展有效的数值计算方法，求解力、电、磁及其耦合动态载荷作用下，微纳米磁电层合材料结构的磁电耦合效应、自由振动和受迫振动以及磁/电响应等特性。如通过哈密顿变分原理得到考虑尺寸效应的微纳米电介质梁的初边值模型，通过有限差分法、有限元单元法等求解动力响应和电介质梁的激化特性，以及层合压电损伤梁的吸附特性，讨论了损伤效应、激化特性、尺寸效应、结构几何参数等对层合电介质结构的非线性静动力学行为的影响，揭示了该类微纳米层合梁的若干非线性静动力学本质特征和失效机理。本项目的研究成果丰富和发展了损伤力学和智能结构非线性静动力学，达到了预期的研究目标。