非线性阻尼、非线性刚度隔振系统的动力学理论和实验研究

Linear vibration isolation systems have a limitation on their performance, especially for low frequencies, which can be overcome passively by using nonlinear stiffness. It has been demonstrated by several researchers that linear isolation systems can be improved upon by using nonlinear damping elements, which can restrain vibration at resonance frequency and have excellent isolation performance at high frequencies. In this project, nonlinear damping could be used in conjunction with nonlinear stiffness to achieve better vibration isolation performance for both force and base excitation. The method of direct separation of motions is used to analyze the single/double stage vibration isolation system with both damping and stiffness nonlinearity. The parameter boundary of both excellent isolation performance and system stability is analyzed using bifurcation theory, and the design parameters could be optimized. The performance of the single/double nonlinear vibration isolator subject to random excitation could be evaluated by the equivalence FPK-Fokker Planck Kolmogorov equation that is transformed by the nonlinear stochastic vibration motion equation. Furthermore, a novel lab-scale two-stage nonlinear vibration isolation system has been designed and constructed. The measurement is used to verify the theoretical model for both base harmonic and random excitation.

高静态低动态非线性刚度隔振系统能够克服线性隔振低频处缺陷，是振动控制领域研究的主要热点之一；非线性阻尼能够抑制线性系统共振频率处响应，同时保持较优高频隔振性能。本项目将非线性阻尼耦合到非线性刚度隔振系统中，根据非线性模态和快慢运动原理，以运动直接分离法与数值计算相结合的手段，探索单层/双层非线性阻尼、非线性刚度隔振系统在谐波激励下的力与位移传递特性。与此同时，应用分叉理论分析获得隔振性能较优和系统稳定的参数边界，优化设计参数。进一步通过求解FPK方程等效非线性随机振动方程来研究单层/双层非线性隔振系统在随机激励下的隔振性能。最后设计和建立非线性隔振试验台，进行基础激励，验证理论模型。通过本项目研究，将明确振动通过非线性阻尼、非线性刚度传递的机理，研究成果将有助于解决低频失稳和高频阻尼恶化的问题，实现被动隔振在某些极端激扰环境下的振动控制。因此，本项目的研究具有至关重要的理论意义和工程价值。

高静态低动态非线性刚度隔振系统，能够克服低频不足，已是振动控制领域研究的主要热点之一。非线性阻尼能够抑制线性系统共振频率处响应，同时保持较优高频隔振性能。本项目在高静态低动态刚度隔振系统基础上引入非线性阻尼提高了隔振性能；发展了直接运动分离法研究高静态低动态刚度隔振非线性阻尼效应；提出了非线性隔振系统传递率的概念，新的定义不但能计及高频分量，使得评价更为准确，而且能够使用于准周期、混沌等非周期情形；发现了非线性隔振系统中的随机共振现象。采用双稳复合板解决了双层非线性刚度实验实现的难题。通过本项目的研究，将明确振动通过非线性阻尼、非线性刚度传递的机理，研究成果将有助于克服低频失稳和高频阻尼恶化的问题，实现被动隔振在某些极端激扰环境下的振动控制。因此本项目的研究具有至关重要的理论意义和工程价值。

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