The thermoelastic damping in a micro-beam of rectangular cross-section is studied using the Euler–Bernoulli beam theory incorporating Lord and Shulman's theory of generalized thermoelasticity with memory-dependent heat conduction. By employing the mode analysis method, explicit formulae for the thermoelastic damping, frequency shift and attenuation are derived. The kernel function, the relaxation time, and the memory time are selected to analyze their effects on thermoelastic damping. The dependence of the inverse quality factor $Q^{-1}$ on the boundary conditions, vibration modes, time delay, aspect ratios, and relaxation time of small-scale mechanical resonators is shown for the memory-dependent heat conduction with ideal, linear, and nonlinear kernels. Numerical results of the $Q^{-1}$ factor are calculated and compared with those based on the Lord–Shulman generalized thermoelasticity and the Lifshitz–Roukes model. The obtained numerical results show that the memory-dependent Lord–Shulman model is more accurate in describing thermoelastic damping than Lifshitz–Roukes' model and the classical Lord–Shulman model.

使用欧拉-伯努利梁理论研究矩形截面微梁中的热弹性阻尼，该理论结合了 Lord 和 Shulman 的具有记忆相关热传导的广义热弹性理论。采用模态分析方法，推导出热弹性阻尼、频移和衰减的明确公式。选择核函数、弛豫时间和记忆时间来分析它们对热弹性阻尼的影响。逆品质因数的相关性${问}^{-1}$在边界条件、振动模式、时间延迟、纵横比和小规模机械谐振器的弛豫时间上，显示了具有理想、线性和非线性内核的记忆相关热传导。的数值结果${问}^{-1}$计算因子并与基于 Lord-Shulman 广义热弹性和 Lifshitz-Roukes 模型的因子进行比较。获得的数值结果表明，与Lifshitz-Roukes 模型和经典的Lord-Shulman 模型相比，记忆相关的Lord-Shulman 模型在描述热弹性阻尼方面更准确。