动力吸振器复合非线性能量阱对线性镗杆系统的振动控制

研究了线性动力吸振器复合非线性能量阱对线性镗杆在外部简谐激励下的振动控制. 忽略镗杆系统中的非线性因素, 建立了附加线性动力吸振器和非线性能量阱的镗杆系统的三自由度运动方程, 研究了附加复合式动力吸振器的镗杆系统的受迫振动. 通过平均法得到了附加复合式动力吸振器的镗杆系统的近似解析解, 并利用数值解验证了近似解析解的准确性, 两者具有很好的一致性. 利用近似解析解详细分析了线性动力吸振器和非线性能量阱的参数对镗杆振动抑制性能的影响. 对给定质量的复合式动力吸振器进行了参数优化, 其中线性动力吸振器参数采用H_∞优化方法的近似解析解进行了优化, 非线性能量阱的阻尼利用系统的近似解析解进行了优化. 分析结果表明, 线性动力吸振器与非线性能量阱组合可以有效抑制线性镗杆系统的振动, 而且采用参数优化后的复合式动力吸振器可以获得更好的减振效果. 通过附加非线性能量阱, 不但可以提高线性动力吸振器的振动抑制效果, 而且还可以提高振动控制系统的鲁棒性. 

VIBRATION CONTROL OF LINEAR BORING BAR BY DYNAMIC VIBRATION ABSORBER COMBINED WITH NONLINEAR ENERGY SINK

The vibration control of linear boring bar system attached with linear dynamic vibration absorber and nonlinear energy sink under external harmonic excitation is studied. By ignoring the nonlinear factors in the boring bar system, the three degree of freedom motion equation of the boring bar system attached with linear dynamic vibration absorber and nonlinear energy sink is established, and the forced vibration of the boring bar system with combined dynamic vibration absorber is studied. The approximate analytical solution of boring bar system with combined dynamic vibration absorber is obtained by means of averaging method. The accuracy of the approximate analytical solution is verified by comparing with the numerical solution, and they are in good agreement with each other. By using the approximate analytical solution, the effects of linear dynamic vibration absorber and nonlinear energy sink parameters on the vibration suppression performance of boring bar are analyzed in detail. Based on the analysis of the influence law of the combined dynamic vibration absorber on linear boring bar system, the parameters of the combined dynamic vibration absorber with given mass are optimized, in which the linear dynamic vibration absorber parameters are optimized by using the approximate analytical solution of H_∞ optimization method, and the damping of nonlinear energy sink is optimized by the approximate analytical solution of the system. The analysis results show that the combination of linear dynamic vibration absorber and nonlinear energy sink can effectively suppress the vibration of linear boring bar system, moreover, the linear boring bar system can obtain better vibration attenuation effect by using the combined dynamic vibration absorber with optimized parameters. By adding nonlinear energy sink can not only improve the vibration suppression effect of linear dynamic vibration absorber, but also improve the robustness of vibration control system. The analysis results can provide a reference for the design of built-in damping boring bar.