Abstract

Size effect is a significant factor for accurate estimation of the thermoelastic damping (TED) in microplate/nanoplate resonators. The actual TED in microstructures/nanostructures is comprehensively affected by various size-dependent mechanisms in the mechanical and thermal field and studying only one of them may lead to one-sided conclusions. In this article, the governing equations of coupled thermoelasticity in a transversely vibrating rectangular plate are derived by the modified nonlocal strain gradient theory and the nonlocal heat conductive law (GK model). Then utilizing the energy approach, a size-dependent TED model for rectangular plates is presented in the form of infinite series. The constitutive boundary conditions are considered to close the nonlocal strain gradient problem in differential form. The silicon material with typical length scale parameters and relaxation time is selected in simulation. The influences of nonlocal elasticity, strain gradient elasticity and nonlocal heat conduction on TED in rectangular plates are investigated under different frequencies, thicknesses and boundary conditions. The simulation results show that the TED expression converges rapidly and the three size-dependent parameters have distinct influences on TED value, critical thickness and critical frequency. By taking advantage of the size effects reasonably, the quality of resonators can be improved.

摘要

尺寸效应是精确估计微板/纳米板谐振器中热弹性阻尼（TED）的重要因素。微观结构/纳米结构中的实际TED受到机械和热场中各种尺寸相关机制的全面影响，仅研究其中之一可能会得出单方面的结论。本文利用修正的非局部应变梯度理论和非局部导热规律（GK模型）推导了矩形振动矩形板中耦合热弹性的控制方程。然后利用能量方法，以无限级数的形式给出了矩形板的尺寸相关的TED模型。本构边界条件被认为可以解决微分形式的非局部应变梯度问题。在仿真中选择具有典型的长度尺度参数和弛豫时间的硅材料。研究了在不同频率，厚度和边界条件下矩形板中非局部弹性，应变梯度弹性和非局部热传导对TED的影响。仿真结果表明，TED表达式收敛迅速，并且三个与尺寸有关的参数对TED值，临界厚度和临界频率有明显的影响。通过合理利用尺寸效应，可以提高谐振器的质量。厚度和边界条件。仿真结果表明，TED表达式收敛迅速，并且三个与尺寸有关的参数对TED值，临界厚度和临界频率有明显的影响。通过合理利用尺寸效应，可以提高谐振器的质量。厚度和边界条件。仿真结果表明，TED表达式收敛迅速，并且三个与尺寸有关的参数对TED值，临界厚度和临界频率有明显的影响。通过合理利用尺寸效应，可以提高谐振器的质量。