Thermoelastic damping is becoming a leading factor for determining the quality of the micromechanical resonators in terms of their sensitivity. The present study is devoted to the analysis of thermoelastic damping of a micro-beam resonator by employing the concept of three-phase-lag (TPL) theory of thermoelasticity in the context of the memory-dependent derivative (MDD). The memory-dependent derivative is characterized by its time delay and the kernel function that can be chosen freely with imposed restrictions. Analytical expressions of thermoelastic damping, attenuation as well as frequency shift have been derived. Computational results for the prominent parameters of micromechanical resonators such as thermoelastic damping, attenuation, and frequency shift are obtained. The influence of the constituents of memory-dependent derivative, i.e. time-delay and kernel functions, on the parameters of the micro-beam resonator has been analyzed through graphical results. Furthermore, numerical results are compared with the results obtained in the absence of a memory-dependent derivative through numerical simulations. The significant role of the memory-dependent derivative has been identified and it has been found that the insertion of the memory-dependent derivative is capable of providing accurate results as compared to the results obtained in its absence.

就其灵敏度而言，热弹性阻尼已成为确定微机械谐振器质量的主要因素。本研究致力于在记忆相关导数（MDD）的背景下，采用三相滞后（TPL）热弹性理论来分析微束谐振器的热弹性阻尼。依赖于存储器的导数的特征在于其时间延迟和内核功能，可以在施加限制的情况下自由选择。推导了热弹性阻尼，衰减以及频移的解析表达式。获得了微机械谐振器主要参数（如热弹性阻尼，衰减和频移）的计算结果。记忆相关导数的成分的影响，即 通过图形结果分析了微束谐振器参数的时间延迟和核函数。此外，将数值结果与通过数值模拟在不存在依赖于存储器的导数的情况下获得的结果进行比较。已经确定了记忆依赖性衍生物的重要作用，并且发现与没有记忆依赖性衍生物的结果相比，插入记忆依赖性衍生物能够提供准确的结果。