Microbeam resonators are widely used due to their scientific and engineering applications. The accurate prediction of thermoelastic damping (TED) is necessary to evaluate the performance of resonators at micro- and nanoscales with less energy dissipation. This article aims to present an analytical method for analyzing TED and dynamic behavior of microbeam resonators based on the Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory. The finite Fourier sine transform and Laplace transform methods are used to solve the coupled thermoelastic equations. The analytical solutions are obtained for deflection and thermal moment of beams. The vibration responses of deflection and thermal moment are established in microbeams with simply supported and isothermal boundary conditions. The responses of deflection and thermal moment in beams are analyzed by comparing the results obtained under the MGT model with the corresponding results under the Lord–Shulman (LS) and Green–Naghdi (GN-III) models. The obtained results show that the amplitudes of deflection and thermal moment are attenuated, and the vibration frequency is increased due to the effect of thermoelastic coupling. It has been observed that the amplitudes of deflection under these three models are approximately the same, while the amplitude of thermal moment under the MGT model is higher than under the GN-III model and agrees with the LS model. It has been further noticed that TED depends on the size of the beams when the thermoelastic coupling effect is considered.

中文翻译：

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基于Moore-Gibson-Thompson广义热弹性理论的微梁谐振腔热弹性阻尼分析

微束谐振器因其科学和工程应用而被广泛使用。热弹性阻尼 (TED) 的准确预测对于评估具有较少能量耗散的微米和纳米级谐振器的性能是必要的。本文旨在提出一种基于 Moore-Gibson-Thompson (MGT) 广义热弹性理论的分析方法，用于分析微束谐振器的 TED 和动态行为。有限傅里叶正弦变换和拉普拉斯变换方法用于求解耦合热弹性方程。获得了梁的挠度和热力矩的解析解。在具有简支和等温边界条件的微梁中建立了挠度和热力矩的振动响应。通过将 MGT 模型下获得的结果与 Lord-Shulman (LS) 和 Green-Naghdi (GN-III) 模型下的相应结果进行比较，分析了梁的挠度和热力矩响应。得到的结果表明，由于热弹性耦合的影响，挠度和热力矩的幅值衰减，振动频率增加。已经观察到，这三种模型下的挠度幅值大致相同，而MGT模型下的热力矩幅值高于GN-III模型下，与LS模型相符。进一步注意到，当考虑热弹性耦合效应时，TED 取决于梁的尺寸。