Dynamic Characteristics Of Nonlinear Vibration Isolation System Based On Wire Rope Isolator

The vibration is the most common phenomenon in our common life and scientific research, such as vibrations of buildings and machines, electromagnetic vibration of radio and optical, engine vibration, complex vibration in chemical reactions, etc. Sometimes we would love to manufacture and use vibration, sometimes we would love to reduce and prevent the vibration. So the vibration isolation becomes the focus point of the mechanic of vibration. Depending on the difference of the mathematical model describing the vibration, the theory of the vibration includes linear vibration theory and nonlinear vibration theory, compared to the nonlinear vibration theory, the linear theory is mature and perfect and the analytical solution can be easily obtained. The linear vibration theory can provide accurate reference for engineering applications, so it is widely used in engineering practice. But with the increasing demand on the isolation, linear vibration has gradually failed to meet the requirements of people. Then the nonlinear vibration isolation came into being, such as air spring isolator, steel wire isolator, rubber isolator, etc.The wire rope isolator is a kind of nonlinear vibration isolator widely used. But in the previous studies of the wire rope isolator, the damping or stiffness of the isolator is often simplified as linear, as a result, the calculation results would always be different with the actual situation, so it is necessary to consider the nonlinear characteristics of the isolator.In this paper, referring to the drum-shaped wire rope isolator, the dynamic equation of the wire rope isolator was established, and the nonlinear dynamic characteristics were studied. The structure of the wire rope isolator, nonlinear stiffness and damping characteristics were introduced. Because of the dry friction the system contained, the model of dry friction was studied, and the Fourier series of dry friction was obtained. Then the free vibration characteristics of the the nonlinear vibration isolation system based of wire rope isolator were studied. According to the differential equation of the vibration isolation system, the numerical method was used to study the singular points of the system, so with the type and the stability of the singular points. Then the paper gave the free vibration response curve and phase trajectories out. Harmonic balance method was used to solve the equation and the first order harmonic approximate solution of the vibration isolution system was obtained. According to the first order harmonic approximate solution, the amplitude frequency reponse curve and the phase frequency were given out. Finally, the transfer rate of the vibration isolation sysstem were studied and the transfer rate of the wire rope vibration isolation system under different conditions was obtained.