【摘要】 研究了由基础振动激励、粘弹性材料隔离的被动隔振体的非线性动力响应.用变形的三次多项式函数表征隔振材料的非线性刚度,用分数阶算子表征阻尼,建立被动隔振体的分数阶非线性动力学方程.用谐波平衡法研究其非线性动力响应特性,得出频率响应方程和幅频曲线,分析了非线性因素对系统的影响.最后,用Floquet理论讨论了周期解的稳态性和稳定区间.分析结果表明,含分数阶算子的动力学模型能够准确地描述粘弹性材料隔振器的动态特性.忽略隔振材料的阻尼非线性、刚度非线性将导致隔振设计和隔振效果分析的明显误差.分析方法和结论为精确进行粘弹性材料的被动隔振设计和隔振效果评价提供理论参考.更多还原

【Abstract】 Research on nonlinear dynamic response of passive vibration isolator,which was excited by foundation vibration and isolated by viscoelastic material was done.Nonlinear stiffness was expressed by the cubic polynomial function of deformation and nonlinear damping was characterized by viscoelastic fractional derivative operator.Then the fractional derivative nonlinear dynamic equation of passive vibration isolator was established.The dynamic response characteristics were analyzed by harmonic balance method and the frequency response equatioin and amplitude-frequency curve were obtained,and furthermore,the influence of nonlinearity on system was analyzed.Finally,the stability and the stable interval of the periodic solution were argued by the Floquet theory.The results indicate that the proposed equation can precisely describe the dynamic characteristics of viscoelastic vibration isolator.The ignorance of nonlinearity of stiffness and damping will result in obvious error.The proposed method provides theoretic reference for design of viscoelastic isolator and the evaluation of its effect.更多还原