Tian Qikeren
College of Electrical Engineering and New Energy, China Three Gorges University, Yichang, 443002, Hubei, People's Republic of China.
Sci Rep. 2025 Apr 22;15(1):13917. doi: 10.1038/s41598-025-98320-5.
The design parameters of the dynamic vibration absorber notably affect the motion space of the main system. A complete new universal method of attaining the explicit exact solution to the optimum damping was proposed to enhance the accuracy of calculating the dynamic vibration absorber's parameters. The interaction between the main system and dynamic vibration absorber taken into account, many exact analytic solutions, for example displacement amplitude amplification factor, stiffness ratio, fixed point coordinate, optimum damping ratio, and phase angle difference, were investigated with the real number form of differential equation of load motion and using L'Hospital first rule in minute detail. Some characteristic parameters of both the main system and dynamic vibration absorber were gotten. The mechanism of the dynamic vibration absorber was analyzed by comparing the displacement amplitude amplification factor between the dynamic vibration absorber and main system. Generally speaking, the dynamic vibration absorber lags behind the main system by certain degrees. The fixed point theory essentially achieves the extreme large value, but not the maximum value, which is a natural shortcoming required to be overcome. The maximum value of the displacement amplitude amplification factor was acquired adopting MATLAB® Version 7.9.0.529 (R2009b). The relative error between the extreme large value and maximum value increases with the increase in the mass ratio. The relative error between the extreme large value and maximum value is 1.3018-10.397% for the optimum damping ratio. The present solutions would be useful to realize and control the precise dynamic characteristics of the main system and dynamic vibration absorber in practice.
动力吸振器的设计参数显著影响主系统的运动空间。为提高动力吸振器参数计算的准确性，提出了一种全新的通用方法来获得最优阻尼的显式精确解。考虑主系统与动力吸振器之间的相互作用，利用载荷运动微分方程的实数形式并详细运用洛必达第一法则，研究了许多精确解析解，如位移幅值放大因子、刚度比、固定点坐标、最优阻尼比和相位角差等。得到了主系统和动力吸振器的一些特征参数。通过比较动力吸振器与主系统之间的位移幅值放大因子，分析了动力吸振器的作用机理。一般来说，动力吸振器在一定程度上滞后于主系统。固定点理论本质上实现的是极大值而非最大值，这是一个需要克服的固有缺点。采用MATLAB® 7.9.0.529（R2009b）版本获取了位移幅值放大因子的最大值。极大值与最大值之间的相对误差随质量比的增加而增大。对于最优阻尼比，极大值与最大值之间的相对误差为1.3018 - 10.397%。本文的解对于在实际中实现和控制主系统及动力吸振器的精确动态特性将是有用的。
