双端固支谐振梁动态响应分析

Dynamic Response Analysis of Double-Ended Resonant Beams

摘要: 谐振式传感器的高动态应用近年来得到越来越多的关注。典型谐振式传感器利用反映被测量的轴向载荷调制谐振梁的固有频率实现这种映射。高动态应用中的核心问题是动态轴向载荷下谐振梁的振动特性。本文以微元法为基础，利用基本的微元力学平衡关系建立了动态轴向力作用下谐振梁振动的数学模型，利用Mathieu方程的一般形式进行分析，引入了等效电路方法进行模型求解。通过对等效电路的仿真，得到了谐振梁在典型动态载荷下的振动响应。此外，本文研究了阻尼对谐振梁的影响，得出阻尼项仅影响谐振梁的振幅，基本不影响谐振梁的频率的结论。

Abstract: The resonant sensor has attracted more attention because of its high sensitivity, small footprint, stability, compatibility with multiple-phase samples. The typical resonant sensor measures reso-nant frequency modulated by axial load to realize mass sensing. Dynamic characteristic is an im-portant factor to evaluate stability of resonant beam, and the key point is to analyze the dynamic response of the resonant beam under dynamic axial load. The article is based on infinitesimal method; mathematical model of vibration of resonant beam impacted by dynamic axial force was established through the resonant beam micro mechanical balance and analyzed through Mathieu equation. Equivalent circuit method was chosen to solve vibration model. The simulation of the circuit shows the dynamic response of resonant beam under the typical axial load. Besides, the article studied the effect of damping on the resonant beam and concluded the damping only influenced on vibration amplitude scarcely on frequency.