基于声子晶体振动机理的周期结构梁的带隙特性研究及ANSYS优化

Study on Band Gap Characteristics of Periodic Structure Beams Based on Phononic Crystal Vibration Mechanism and ANSYS Optimization

摘要: 为研究精密高精密加工中的振动影响因素，通过把微观晶体结构应用到宏观结构梁上，以欧拉梁的理论模型为基础，采用欧拉–伯努利梁方程(Euler-Bernoulli Beam Theory)进行理论分析。使用ANSYS进行建模、仿真和误差分析，对宏观周期结构振动带隙产生的关键因素、阶数和幅值的决定因素进行研究及优化。结果表明，在不同材料、截面、阻尼等要素的周期结构中，可以很容易地发现：改变周期结构参数和振子种类可以有效减振，并且在一定频带区间可以获得频率低、衰减大的局域带隙。根据理论分析和仿真结果得出，一组元变截面和短梁周期结构的振动幅值从1e-4降低到1e-6左右，同时在匹配固有频率150~240 Hz之间时易出现突变的局域振动带隙。因此对于精密和高精密加工设备可以选择合适的变截面周期机构设计、周期数、阻尼和泊松比，以降低加工过程中的动态误差。

Abstract: In order to study the vibration influencing factors in precision and high-precision machining, the Euler-Bernoulli beam theory is used for theoretical analysis by applying micro-crystal structure to macro-structure beam and based on the theoretical model of Euler beam. ANSYS is used for model-ing, simulation and error analysis to study and optimize the key factors, order and magnitude of vi-bration band gap of macro-periodic structure. The results show that in the periodic structure of dif-ferent materials, sections, dampers and other elements, it is easy to find that changing the periodic structure parameters and oscillator types can effectively damp the vibration, and a local band gap with low frequency and large attenuation can be obtained in a certain frequency band range. Ac-cording to theoretical analysis and simulation results, the vibration amplitude of a variable cross-section unit and short beam periodic structure is reduced from 1e-4 to about 1e-6, and abrupt local vibration band gap is prone to occur when matching the natural frequency between 150~240 Hz. Therefore, for the precision and high-precision machining equipment, the appropriate variable section periodic mechanism design, cycle number, damping and Poisson ratio can be selected to reduce the dynamic errors in the process of machining.