| 一种准零刚度被动隔振系统的非线性共振响应分析 |
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| 引用本文： | 彭献,张施详.一种准零刚度被动隔振系统的非线性共振响应分析[J].湖南农业大学学报(自然科学版),2011,38(8):34-39. |
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| 作者姓名： | 彭献 张施详 |
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| 作者单位： | （湖南大学 机械与运载工程学院，湖南 长沙410082） |
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| 摘 要： | 分析了一种机构的负刚度特性和它与线性主弹簧并联后而成的隔振系统的准零刚度特性，推导了准零刚度被动隔振系统的主谐波共振、亚谐波共振和超谐波共振的幅频特性表达式.结果表明，机构的负刚度区域随弹簧的初始变形与杆长的比值增大而变宽；隔振系统的准零刚度区域随主弹簧的刚度与机构中的弹簧总刚度的比值以及机构中的弹簧初始变形与杆长的比值增大而变宽；经比较发现，本文推得的被动隔振系统的同一种谐波共振幅频特性与杜芬方程的幅频特性均存在较大偏差.因此，对于这类被动隔振系统的运动微分方程，若以位移激励的幅值与激励频率平方的乘积代替单位质量的激励力幅值按杜芬方程的解来处理谐波共振问题将会带来较大误差.
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| 关 键 词： | 负刚度 准零刚度 非线性 共振响应 幅频特性 |
Nonlinear Resonance Response Analysis of a Kind of Passive Isolation System with Quasi-zero Stiffness |
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| Institution: | (College of Mechanical and Vehicle Engineering, Hunan Univ, Changsha, Hunan410082, China) |
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| Abstract: | The negative stiffness properties of a mechanism and the quasi-zero stiffness properties of a vibration isolation system of the mechanism after being merged into the linear main spring were analyzed. The main harmonic, sub-harmonic and super- harmonic resonance amplitude-frequency response expressions of passive isolation system with quasi zero stiffness were derived. The results have shown that the negative stiffness region broadens as the ratio of the initial deformation of the spring to the length of the bar increases. The quasi-zero stiffness region of the vibration isolation system broadens as the ratio of the stiffness of the main spring to the total stiffness of the spring in the mechanism and the ratio of the initial deformation of the spring to the length of the bar in the mechanism increase. Compared with the amplitude-frequency characteristics of Duffing equation, the corresponding harmonic response amplitude-frequency characteristics of the passive vibration isolation system demonstrate great deviation. To the motion differential equations of this kind of passive isolation system, there is comparatively larger deviation when the product of the displacement exciting amplitude and the square of exciting frequency replace the exciting force amplitude of unit quality as the solution of Duffing equation. |
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| Keywords: | negative stiffness quasi zero stiffness nonlinear resonant responses amplitude frequency characteristics |
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