具有中空结构的双层圆截面微梁热弹性阻尼模型

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (20) : 278-284.

论文

罗志军1，李普1，方玉明2

作者信息 +

Thermoelastic damping in hollow bilayered microbeam with circular cross-section

LUO Zhijun1, LI Pu1, FANG Yuming2

Author information +

文章历史 +

摘要

热弹性阻尼是热弹性体内部固有的能量损耗机制，对微谐振器的品质因数有重要影响。针对弯曲振动的具有中空结构的双层圆截面微梁，提出一种热弹性阻尼解析模型。利用格林函数法求得微梁中的温度场函数，由温度场函数计算出每一层的能量损耗与储存的最大弹性势能，进而建立无穷级数形式的热弹性阻尼解析模型；对比微梁的FEM模型计算的热弹性阻尼；与Zener单层圆截面微梁模型和TR中空单层圆截面微梁模型对比；探讨金属镀层和体积比对热弹性阻尼的影响。结果表明：FEM模型和当前解析模型的计算结果基本吻合，验证了当前解析模型的有效性；当前解析模型只保留第一项时，热弹性阻尼的计算结果与Zener梁模型和TR梁模型的计算结果一致；金属镀层会增加微梁的热弹性阻尼；对于细长SiC/Si结构微梁，当体积比不变时，热弹性阻尼峰值不变，但其峰值频率会随着微梁体积的增加而减小。

Abstract

The thermoelastic damping (TED) is the inherent energy loss mechanism in the thermal elastomer, which has an important influence on the quality factor of the micro resonators.An analytical model of thermoelastic damping was proposed for the hollow bilayered microbeam with circular cross-section in flexural vibration.Firstly, the temperature field function in the microbeam was obtained by the Green's function method, and the energy loss and the maximum elastic potential energy stored were calculated by the temperature field function, then the analytical model of TED in infinite series form was established.Secondly, the FEM model of microbeam was established to verify the validity of the present analytical model.In addition, compared with the Zener's model and the TR's model, it was found that when the present analytical model only retains the first term, the TED is consistent with the results of the Zener's model and the TR's model.Finally, the effect of metal coating and volume ratio on TED was discussed.The results show that: the metal coating can increase the TED; for the slender microbeam composed by SiC and Si, the peak value of the TED is constant when the volume ratio is constant, but the peak frequency will decrease with the increase of the volume of the microbeam.

导出引用

罗志军，李普，方玉明. 具有中空结构的双层圆截面微梁热弹性阻尼模型[J]. 振动与冲击, 2021, 40(20): 278-284

LUO Zhijun, LI Pu, FANG Yuming. Thermoelastic damping in hollow bilayered microbeam with circular cross-section[J]. Journal of Vibration and Shock, 2021, 40(20): 278-284

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