Tian Hongliang, Liang Xixiao, Du Xuan
College of Mechanical and Power Engineering, China Three Gorges University, Yichang, Hubei, The People's Republic of China.
PLoS One. 2024 Dec 31;19(12):e0315289. doi: 10.1371/journal.pone.0315289. eCollection 2024.
The design parameters of the dynamic vibration absorber significantly affect the motion performance of the main vibration system. The Brock's approaching zero method was improved as approaching the fixed point frequency method. A general method of obtaining the explicit exact solution to the optimum damping ratio was presented to improve the accuracy of calculating the dynamic vibration absorber's optimum parameter. Some exact closed-form solutions, for example displacement amplitude gain, fixed point coordinate, and optimum damping ratio, were deduced with the real number form of differential equation of load motion and employing L'Hospital first rule. Many computational parameters of the main vibration system were attained. The fixed point theory essentially computes the extreme large value, not the maximum value. The numerical simulation results of the present paper's absorber are closer to the vibrational experimental results than those of the Ormondroyd absorber and Lanchester absorber. Moreover, the present paper's absorber has larger band width than the Ormondroyd absorber and Lanchester absorber. The current answers may be applicable to realize and control the accurate dynamic performances of the main vibration system and dynamic vibration absorber in operation.
动力吸振器的设计参数对主振动系统的运动性能有显著影响。将布罗克趋近零点法改进为趋近固定点频率法。提出了一种获得最优阻尼比显式精确解的通用方法，以提高动力吸振器最优参数计算的准确性。利用载荷运动微分方程的实数形式并采用洛必达第一法则，推导了一些精确的闭式解，如位移幅值增益、固定点坐标和最优阻尼比。获得了主振动系统的许多计算参数。固定点理论本质上计算的是极大值，而非最大值。本文吸振器的数值模拟结果比奥蒙德罗伊德吸振器和兰彻斯特吸振器的更接近振动实验结果。此外，本文的吸振器比奥蒙德罗伊德吸振器和兰彻斯特吸振器具有更大的带宽。当前的答案可能适用于实现和控制运行中主振动系统和动力吸振器的精确动态性能。
