隔振和能量采集一体化非线性设计及动力学研究

Simultaneous use of a mechanical structure as a vibration isolator and an energy harvester provides a new view point for some engineering problems such as the design of the vibration reduction. The application on the power self-provided vibration control of aerospace engineering has put forward the imperative requirement. To increase the work efficiency of the integration system, their dynamical characteristics should be fully understood. The corresponding scientific issue is nonlinear update of the vibration model for the composite material structure, which is a significant topic in dynamics. In this project, a piezoelectric bi-stable laminate plate could be designed for the integration of nonlinear vibration isolation and nonlinear energy harvesting. Approximate analysis, numerical simulations, and experimental validations will be performed to explore the dynamic characteristics of the integration system. The resonance conditions required by efficient integration of vibration isolation and energy harvesting will be clarified, and the effects of nonlinearity will be examined. Investigation of stability margin and attraction domain could enhance the robustness of the integration system. Optimizing the topology configuration of the lattice structure enhance the performance of integration system in order to be adapt to the multi-point excitation environment. Vibration experiments will be done by use of the shaking table with 6 degrees of freedom excitation. Nonlinear jump based parameters identification is applied to validate the theoretical models, methods and results. The project outcome will enrich the approximate analytical approaches for vibrating systems with strong nonlinearities, understand interaction mechanisms of vibration regulation and energy transfer, and promote the growth of the field of dynamics and control; meanwhile the outcomes will lay the theoretical foundation of designing and optimizing the integration of vibration isolation and energy harvesting.

基于隔振并将振动能量收集利用的思路提出隔振和能量采集一体化概念，其应用在航空航天工程振动控制自供能领域提出了迫切需求。为深入认识隔振和能量采集器的动力学特性、提高设计水平，相应的科学问题为复合材料结构振动非线性修正，是动力学领域的前沿课题。本项目针对非线性隔振和能量采集一体化问题，设计压电双稳态层合板的负刚度结构，运用近似解析分析、数值仿真和实验验证，明确隔振和能量采集一体化实现所必要的共振关系及其非线性特性，并从稳定性裕度、吸引域角度解决高效性、稳定性和鲁棒性不可兼得的难题。通过点阵结构拓扑优化，揭示群体性同步行为和一体化效率间关系，以适应多点激励环境。设计六自由度激励振动台实验，利用非线性跳跃理论，识别结构参数，验证理论模型。研究成果将发展强非线性振动解析分析方法，认识振动传递和能量采集两者共同的非线性调控机理，推动动力学与控制学科的发展，为设计和优化隔振和能量采集一体化奠定理论基础。

基于隔振并将振动能量收集利用的思路提出隔振和能量采集一体化概念，为深入认识一体化系统动力学特性、提高设计水平，开展了力电耦合系统振动非线性设计理论、计算和实验，是动力学与控制领域的重要研究方向。本项目针对隔振和能量采集一体化非线性设计，发展了强非线性微分方程边值问题的半解析方法，获得了难以解析求解的非线性多模态输出频响函数，通过非线性频响表征运动连续体的振动模态间的能量转移。建立了基于正交六自由度、双稳态层合板和力电耦合超材料等几种一体化系统的非线性力电耦合模型，运用近似解析分析、数值仿真和实验验证综合研究方法，揭示了隔振和能量采集一体化实现所必要的共振关系及其非线性特性，并从稳定性裕度、吸引域角度提高隔振和能量采集性能。通过点阵超材料结构拓扑优化，揭示了群体性同步行为和一体化效率之间映射关系，以适应多源激励环境。研究成果将发展振动能量非线性调控的基础理论和分析方法，推动动力学与控制学科的发展，为设计和优化国家重大工程隔振和能量采集一体化奠定理论基础。

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