摘要
分别使用非线性恢复力、非线性阻尼替代惯容减振系统中的线性恢复力、线性阻尼,并考虑摩擦力的影响,提出了混联Ⅱ型惯容非线性能量阱.建立了主系统的动力学方程,利用谐波平衡法求解系统在简谐激励下的幅频响应曲线.采用弧长算法和数值法相结合的方法研究了系统的惯质比、非线性阻尼、非线性刚度和摩擦力单个参数对其减振性能的影响.发现非线性刚度和非线性阻尼数值的增大会使峰值先减小后增大,不同的是,前者幅频响应曲线逐渐向右上方向弯曲,后者产生峰值的位置向低频段转移.分析了惯质比、非线性阻尼、非线性刚度3种参数两两组合下对系统减振效果的影响.研究表明,在激励幅值为0.005 m时,惯质比和阻尼同时变化减振效果最好:当ε=0.1时,系统主结构位移峰值的最小值约为0.01 m;而在参数ε=0.001时,整体取值范围内其最大值约为0.061 m;当惯质比取得最佳值0.1时,非线性阻尼和非线性刚度κ21的取值范围变大.在摩擦力的作用下,系统的最大幅值都有不同程度的增加.上述研究可为振动系统减振的研究提供参考.
Abstract
A serial-parallel-Ⅱ inerter nonlinear energy sink was proposed through replacement of the linear re-storing force and linear damping with the nonlinear restoring force and nonlinear damping in inertial vibration reduction systems,in view of the effects of friction.The dynamic equation for the main system was established,the amplitude-frequency response curves of the system under the base simple harmonic excitation were solved with the harmonic balance method.The effects of the inertia ratio,nonlinear damping,nonlinear stiffness and friction on the vibration damping performance of the system were studied with the arc length algorithm and the numerical method.The results show that,with the increase of the nonlinear stiffness and nonlinear damping,the peak value will first decrease and then increase.The difference is that the amplitude-frequency response curve of the former gradually bends to the upper right direction,and the position of the peak value of the latter shifts to the lower frequency band.The actions of 3 parameters of the inertial ratio,nonlinear damping and non-linear stiffness,on the damping effects of the system were analyzed.The research indicates that,with an exci-tation amplitude of 0.005 m,the vibration reduction effect will be the best when the inertia ratio and damping change simultaneously.For ε=0.1,the minimum value of the peak displacement of the main structure of the system will be about 0.01 m,while for ε=0.001,the maximum value within the overall value range will be ap-proximately 0.061 m,and the amplitude damping ratio will be 97.1％and 82.1％,respectively.When the inertia ratio reaches optimal value 0.1,the nonlinear damping range and nonlinear stiffness κ21 will grow larger.Under friction,the maximum amplitude of the system will have different degrees of increases.The research results provide a reference for the study on structural vibration reduction.
维普
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