计入基础运动的环状周期结构振动特性分析

Vibration Characteristic Analysis of Ring-Shaped Periodic Structure Incorporating Basic Movement

研究了一类工程领域广泛应用的环状周期结构的弹性振动特性,重点分析了基础运动对弹性振动稳定性和固有频率分裂的影响.首先在随动坐标系下采用Hamilton原理建立了计入基础运动和面内切向及径向弹性振动的偏微分形式的动力学模型.然后,应用伽辽金方法将其离散得到一组常微分动力学方程.根据经典振动理论,得到了系统特征值的数学表达.最后采用数值方法计算了系统的特征值.根据特征值的实虚部取值预测了不稳定域和固有频率分裂规律,并用Runge-Kutta法给出稳定性的数值验证.该研究为陀螺仪等呈现平面或空间基础运动的环状周期结构的动态性能的改善提供了理论借鉴.

The elastic vibration characteristic of a ring-shaped periodic structure intensively used in engineering prac-tice was examined,where the focus was on the effect of basic movement on elastic vibration stability and naturalfrequency splitting. Firstly,a partial differential dynamic model incorporating basic movement and in-plane tangen-tial as well as radial elastic vibrations was established in moving frame using Hamilton＇s principle. Then,a set of ordinary differential dynamic equations were formulated using Galerkin method. The mathematical expressions of eigenvalues of the system were derived according to the classical vibration theory. Finally,the eigenvalues were cal-culated by use of numerical method. Unstable areas and the rules of natural frequency splitting were predicted by means of real and imaginary parts of eigenvalues. The stability was verified by numerical calculation with Runge-Kutta method. This research provides theoretical reference for the dynamic performance improvement of microgyro-scope or other ring-shaped periodic structures undergoing two- or three-dimensional basic movement.