微尺度压电层合细长结构热力电多场耦合动力学行为

Microscale piezoelectric laminated slender structures are kernel components of micro electro mechanical systems (MEMS). The complex vibrations of microscale piezoelectric structures comprise coupled dynamical effects of thermal field, elastic field and electrical field. Through analyzing the coupled dynamical behaviors of microscale piezoelectric laminated slender structures, it will be useful to design better MEMS, to avoid failure and to improve work efficiency. However, to the best of authors’ knowledge, there are only few reports published in literature concerning coupled vibration problems of microscale piezoelectric laminated slender structures. Moreover, the effects of cracks or defects embraced in the slender structures do not causing attention. In view of these situations, this project intends to study the coupled piezothermoelastic vibrations of microscale piezoelectric laminated slender structures. Several physical factors temperature, microscale, piezoelectric and cracks will be considered in the coupled dynamical systems of microscale piezoelectric laminated slender structures. More specifically, the generalized thermoelastic theory will be used to describe the heat transfer process in the microscale structures; the equivalent circuit model will be employed to represent the electric field in the microscale structures; the equivalent torsional spring model will be utilized to characterize the mechanical characters of the cracks in the slender structures, and the non-local elastic theory and beam theory will be used to describe the strains and elastic characters of the microscale slender structures. The obtained coupled dynamical systems will be solved by the Green’s function method, the finite element technique and the experimental approach. Then, the interactions among thermal field, elastic field and electrical field will be discussed. Transformation rules among several different energies will be revealed. The quantitative indexes of the contributions of the factors temperature, microscale, piezoelectric and cracks on the electric power conversion efficiency will be studied and the optimization methods for these quantitative indexes will be obtained in this study. The research achievements of this project will gain a deeper insight into the vibration characteristics of microscale piezoelectric structures, and provide theoretical supports for the design of MEMS.

微尺度压电层合细长结构是微机电系统（MEMS）的核心构件。微尺度下，压电层合结构的振动将存在热力电等多场耦合作用。通过研究微尺度压电层合细长结构多场耦合振动可以改善MEMS设计，避免故障，提高工作效率，然而目前却少见针对此类问题的报道。此外，含裂纹的微尺度压电层合细长结构还未得到关注。因此本项目拟开展微尺度压电层合细长结构热力电多场耦合振动研究。综合考虑热、微尺度、压电和裂纹等因素，借助广义热弹性理论描述微尺度传热，利用等效电路表述电场，采用等效扭簧模拟裂纹，使用非局部弹性和梁理论刻画结构应变和弹性，建立微尺度压电层合细长结构多场耦合振动的动力学方程。利用格林函数法、有限元法和实验分析该多场耦合动力学模型，讨论各物理场间相互作用，揭示不同能量间转化规律，量化各因素对电能转化率的贡献，并得到针对各量化指标的优化方法。项目研究成果将加深对微尺度压电结构振动特性的认识，为MEMS的设计提供参考。

微尺度压电层合细长结构是微机电系统（MEMS）的核心构件。基于Eringen非局部弹性理论、经典瑞利梁模型和第三类Green-Naghdi模型，研究了微/纳米梁的热弹性耦合强迫振动，得到了耦合动力系统的显式解，研究得到微/纳米梁的基本固有频率随小尺度参数增加而减小、微/纳米梁与宏观梁振动规律的差异等结论；完成了具有可变长度尺度参数的双向功能梯度微梁的自由振动和屈曲的工作；进一步解决了热环境中磁-电-弹性层合梁的非线性弯曲和大振幅振动问题，导出了关于温度场、磁势、非线性频率和弯曲平衡路径的解析表达式。得到结论：温度波动对层合梁的非线性与线性的频率比影响很大、温度的分布和材料叠层决定了层合梁热力矩的方向和大小；研究了具有两种阻尼效应的压电层合梁的热电弹三场耦合的强迫振动，研究结果讨论了对流热系数对电压的影响，以此确定了最佳传热系数，同时也验证了悬臂梁比简支梁更加适合所压电能量采集器；通过格林函数法，推导了双参数地基上输油管道在简谐力作用下受迫振动的解析解，研究可知对于弹性基底截面，固有频率和临界速度随着两个基础参数的增加而增加；另外研究了轴向压缩荷载作用下Timoshenko双梁系统的强迫振动的格林函数解，通过格林函数方法推导了考虑阻尼效应情况下Timoshenko曲梁的强迫振动的解析解；同样通过格林函数法和采用局部柔度模型，获得了具有两种阻尼的多裂纹Timoshenko梁的强迫振动的解析解，还研究了被腐蚀的Euler-Bernoulli海洋管道模型在海波激励下的动力学响应。研究结果对修复、控制和诊断受损结构的技术大有帮助；延伸研究了在湿热环境下受气动力作用的旋转复合薄壁梁的弯曲-弯曲耦合振动以及亚音速气流和湿热环境对旋转复合材料层合圆柱壳行波振动的联合影响。本项目的研究成果对MEMS有一定的参考价值。