动态轴向载荷下谐振梁振动响应分析

在航空航天飞行控制中，为实现关键参数的高精度高动态测量，急需发展具有快速响应特性的谐振式传感器。谐振式传感器本质上是输入与谐振器振动状态之间的映射。这种映射一般通过跟随输入的轴向载荷调制谐振梁的固有频率实现。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响应。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行为的数学模型。此模型比Mathieu方程的适用面更广，在一般假设下更难以进行解析或数值求解。为此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，得到了谐振梁在多种典型动态载荷下的振动响应。动态轴向载荷对于谐振梁的作用具有强烈的非线性和独特的规律，值得进一步深入研究探讨。

Resonant beam vibrating response under dynamic axial load analysis

In the field of aero and space flight control,in order to realize high accuracy and high dynamic measure?ment of key parameters,it is urgent to develop resonant transducers with fast response feature. A resonant sensor is essentially a mathematical mapping between the input and the vibration state of the resonator. This mapping is usu?ally implemented by modulating the natural frequency of the resonant beam by an axial load following the input. The core issue in high dynamic applications is the vibration response of the resonant beam under dynamic axial load. The mathematical model of resonant beam vibrating behavior under dynamic axial load was established through the basic micro element mechanical balance relationship. This model can be applied in more fields than the Mathieu equation,and it is more difficult to be solved analytically or numerically. Thus the equivalent circuit meth?od was introduced to solve the model. By simulation on the equivalent circuit,vibration response of resonant beam under several typical dynamic loads was obtained. Dynamic axial load has a strong nonlinear effect on the resonant beam with unique rules,indicating that this problem is valuable for further research and discuss.