A comprehensive 3-D finite element formulation for the coupled thermoelastic system is proposed based on the Total Lagrangian framework to study the thermoelastic damping (TED) in small scale structures. The proposed formulation takes into account geometric nonlinearity because of large deformation and material nonlinearity where material parameters are functions of temperature and strain field. Using the proposed finite element formulation, the TED quality factor is obtained for 1-D rod undergoing longitudinal vibrations using the eigenvalue analysis. We first validate the accuracy of the finite element implementation with previously known theoretical and numerical results. Subsequently we demonstrate the utility of the proposed numerical framework to study the effect of geometric nonlinearity, temperature and strain dependent material nonlinearity on the thermoelastic damping.In addition, the effect of internal/ external heating and different thermal boundary conditions on TED is discussed

翻译：本文基于完全拉格朗日框架，提出了一种耦合热弹性系统的三维有限元通用公式，用于研究微尺度结构中的热弹性阻尼。该公式同时考虑了大变形引起的几何非线性，以及材料参数随温度场和应变场变化的材料非线性。通过所提出的有限元公式，采用特征值分析方法，我们获得了承受纵向振动的一维杆件的热弹性阻尼品质因子。首先，我们通过已有理论解和数值结果验证了有限元实现的准确性。随后，我们展示了所提数值框架在研究几何非线性、温度相关及应变相关的材料非线性对热弹性阻尼影响方面的实用性。此外，本文还讨论了内部/外部热源以及不同热边界条件对热弹性阻尼的影响。