非线性增强波纹管液力惯容隔振器的建模及隔振性能研究
Modeling and isolation performance of a nonlinear enhanced bellow-type hydraulic inerter-based vibration isolator
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摘要: 针对低频线谱振动隔离难点,提出了一种非线性增强的波纹管液力惯容动力反共振隔振装置。建立了该非线性增强系统的双稳负刚度的准静态模型及非线性动力学模型,研究了几何尺寸、弹性系数等参数对系统非线性刚度特性的影响,发现负刚度增强结构仅对隔振器刚度的非线性程度起调控作用,而不改变其承载能力和静变形。进而开展隔振性能分析工作,推导了基准线性系统在力激励作用下的振动传递率,并研究了无量纲化参数惯性质量比、有效面积比、阻尼比三个绝对量对传递率特性的影响规律;采用平均法求解了增强非线性系统的动力学响应,基于等效线性化刚度给出了非线性增强系统传递率解析求解方法和步骤,并与数值仿真结果对比,结果发现解析传递率与数值结果较为吻合;对非线性负刚度增强的液力惯容隔振系统的传递率特性开展了比较性研究,结果表明,引入双稳负刚度可以降低隔振系统的共振频率和反共振频率,通过设计合理的惯性质量参数,可在低频段获得优越的宽带隔离特性。Abstract: A nonlinear enhanced bellows-type hydraulic inerter-based antiresonance vibration isolator is proposed for low-frequency line spectra vibration isolation. The nonlinear dynamic model of the enhanced system and the quasi-static model with bistable negative stiffness are established. The influence of parameters such as geometric dimensions and elastic coefficients on the nonlinear stiffness characteristics of the system is studied. It is found that the structure with negative stiffness enhancement only regulates the extent of nonlinear stiffness without changing the load-bearing capacity or static deformation. Subsequently, an estimation analysis of vibration isolation performance is conducted. The vibration transmissibility of the degraded linear system under force excitation is studied, and the effects of non-dimensional parameters, including the inertial mass ratio, effective area ratio, and damping ratio, on the transmissibility characteristics are analyzed. The dynamic response is solved by using the averaging method, and the analytical solution steps for the transmissibility of the nonlinear enhanced system are given based on the equivalent linearized stiffness. The analytical results are validated by comparing them with numerical simulation results, showing small relative errors, and thus can be used for design purposes. A comparative study is conducted on the transmissibility characteristics of the nonlinear negative stiffness enhanced hydraulic inerter-based vibration isolation system. The results indicate that the introduction of a bi-stable negative stiffness can lower the resonance and anti-resonance frequencies of the isolation system. By designing appropriate inertial mass parameters, it is possible to achieve superior wideband isolation effectiveness in the low-frequency range.