分数阶非线性隔振系统幅频特性及稳定性研究  

Study on Amplitude-frequency Characteristics and Stability of Fractional Order Nonlinear Vibration Isolation Systems

作　　者：屈鸣鹤 吴少培 俞力洋 李国芳[1] 丁旺才[1] QU Minghe;WU Shaopei;YU Liyang;LI Guofang;DING Wangcai(School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070

出　　处：《噪声与振动控制》2023年第3期40-46,共7页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(11962013,12162020,11732014);甘肃省青年科技基金资助项目(21JR7RA335);。

摘　　要：建立分数阶非线性Zener模型描述橡胶隔振系统的力学特性,采用高阶谐波平衡法求解系统响应的近似解,并与数值方法所得结果进行比较,给出系统发生鞍结分岔的边界条件,分析参数对系统多态共存频带以及幅频响应的影响规律。研究表明:不同激励频率下的系统动力学响应存在周期运动多样性;分数阶的系数增大会导致系统主共振和超谐波共振的峰值降低;随着分数阶的阶数增大,系统主共振幅值先降低后升高,三次超谐波共振幅值降低,而更高次超谐波共振幅值先升高后降低;系统在超低频区也存在有效隔振的情况,考虑高次超谐波响应的隔振性能与实际情况更为接近。The fractional nonlinear Zener model is established to describe the mechanical characteristics of rubber vibration isolation systems.The system response is solved by high-order harmonic balance method and the results are compared with those of numerical methods.The boundary conditions of saddle-node bifurcation of the system are given and the influence of parameters on the multi-state coexistence frequency band and amplitude-frequency response of the system are analyzed.The results show that the dynamic response of the system under different excitation frequencies has the diversity of periodic motion.With increase of fractional coefficient,the peak values of main resonance and super-harmonic resonance of the system decreases.With increase of fractional order,the main amplitude of the system decreases first and then increases,the amplitude of the third-order harmonic wave decreases and the amplitude of higher-order harmonic wave increases first and then decreases.The system also has effective vibration isolation in the low frequency region.The vibration isolation performance considering high-order super-harmonic response is closer to the actual situation.

关 键 词：振动与波 分数阶微分 非线性Zener模型 超谐波共振 隔振性能 

分 类 号：O322[理学—一般力学与力学基础]