功能梯度材料微梁板的热弹性阻尼研究

On the basis of theory of thermoelsatic coupling dynamics for non-homogenous materials, thermoelastic damping of functionally graded material micro beam and plate resonators will be investigated. Comprehensively considering the effects of thermoelastic coupling, graded variation of the material properties, thermal relaxion in the heat conduction and size dependant effects, dynamic equations governing thermoelastic coupled vibration of the functionally graded material micro beams and plates will be established. Characteristics of internal fraction and frequency dissipation in the process of vibration of the micro structures will be studied by analytical approach in conjunction with numerical simulation. Effective methods will be investigated to solve the mixed boundary value problem of coupled partial differential equations with variable coefficients to arrive at analytical, semi-analytical or numerical solutions for the complicated dynamic system including internal dissipation. Quality factor to evaluate the thermoelastic damping and the frequency shift of the system will be obtained and the level of energy dissipation arised from the irreversible thermal motion in the thermoelastic coupling vibration of the micro structures will be examined quantitively. Furthermore, we will reveal the regular pattern how the frequency and quality factor are affected by the material inhomogeneity and may find new characteristics of thermoelastic damping different from those of the homogenous micro structures. Finally, we will explore the possibility to reduce thermoelastic damping by optimal design of material gradient along the thickness direction. The research results will be helpful for us to further understand the energy dissipation mechnanism and characteristics of the non-homogenous micro structures and will have theoretical significance and application value for the design of new type of micro vibration structural components.

基于非均匀材料热弹性耦合动力学基本理论，研究功能梯度材料微梁板的热弹性阻尼特性。综合考虑热弹耦合效应、材料性质梯度变化、热传导过程中的热松弛效应以及材料微尺度效应，建立功能梯度材料微梁板热弹耦合振动的动力学控制方程。采用解析与数值模拟相结合的方法研究功能梯度微梁板在谐振动过程中因热弹耦合导致的内摩擦和频散特性。研究热弹耦合变系数偏微分方程混合边值问题的有效求解方法，寻求具有内耗散的复杂动力系统的解析解、半解析解和数值解。重点分析热弹耦合振动过程中不可逆热流引起的能量耗散水平，计算评价热弹性阻尼的品质因子和频移，揭示材料性质梯度变化对频率及品质因子的影响规律，发现不同于均匀材料微结构热弹性阻尼的新现象和特性，探索通过材料性质沿厚度梯度变化的优化设计减小微梁板热弹性阻尼的可能性。成果有助于进一步认识非均匀微结构的热弹性耦合耗能特性及规律，对新型微振动器件的设计具有一定的理论意义和应用价值。

热弹性阻尼作为一种内部能量耗散机制，当谐振器处于微/纳尺度时会成为微/纳电机系统的主要耗能方式，并且不能通过改善外部条件来降低。功能梯度材料是一种材料组分的体积分数可在指定方向连续变化的新型非均匀复合材料。由于功能梯度具有相比均匀材料更加优异的材料性质，功能梯度谐振器在微/纳电机系统中将会得到越来越多的实际应用。微/纳谐振器的力学模型大多可简化为梁或板。本项目基于非均匀材料热弹性耦合动力学基本理论，研究了功能梯度材料微梁板的热弹性阻尼特性。综合考虑热弹耦合效应、材料性质梯度变化、热传导过程中的热松弛效应以及材料微尺度效应，建立了功能梯度材料微梁板热弹耦合振动的动力学控制方程。采用分层均匀化方法研究了功能梯度微梁板在谐振动过程中因热弹耦合导致的内摩擦和频散特性。研究了热弹耦合变系数偏微分方程混合边值问题的有效求解方法，获得了具有内耗散的复杂动力系统的解析解、半解析解和数值解。重点分析了热弹耦合振动过程中不可逆热流引起的能量耗散水平，得到了评价热弹性阻尼的品质因子和频移，揭示了材料性质梯度变化对频率及品质因子的影响规律，发现了不同于均匀材料微结构热弹性阻尼的新现象和特性，提出了通过材料性质沿厚度梯度变化的优化设计减小微梁板热弹性阻尼的方法。本项目研究成果对进一步认识非均匀材料谐振器的耗能机理具有理论意义，对新型高品质谐振器的研究和设计有参考价值。