双端固定振荡石英梁加速度计的动力分析

Dynamical analysis of double-end-fixed oscillating quartz beam accelerometer

为了研究双端固定(ZYw)+2°石英梁加速度计受轴向预力时其共振频率的变化,将石英梁视为欧拉梁,并考虑石英的压电效应,利用压电弹性体的汉密顿原理来推导运动方程式,将石英梁位移解代入边界条件,解析得到轴向预力与共振频率关系的正解。结果表明,频率与轴向预力之间存在线性范围,其可作为加速度计的输入—输出关系。由前三阶模态频率变化图发现,张力会使频率增大,压力会使频率减小,且压力过大会造成梁屈曲(buckling)。可利用共振频率与轴向预力的线性关系作为加速度计的工作原理来检测车辆的加速度。

In order to investigate the effect of the axial force on the natural frequencies of an accelerometer made of double-end-fixed oscillating（ ZYw） ＋ 2° quartz beam,the slender quartz beam is modeled as Euler ＇s beam and the piezoelectric effect of Quartz is also considered. The Hamilton＇s principle for the piezoelectric and elastic body is used to derive the equations of motion.Based on this model and the use of boundary conditions,the relation between the frequencies and axial forces can be obtained by exact solution. The solution shows that there is a linearly proportional range between the frequency and axial force,which can be serviced as the-input-output relation of an accelerometer. The results of first three modes reveals that tensional force increases the frequencies,while compressive force decreases them,larger compressive force will cause the beam buckling. The linear relation between the frequencies and axial force is used as the working principle for the accelerometer to detect the acceleration of vehicles.