| Vibration is a widespread and important phenomenon in nature, which hasthe common objective law and unified mathematical expression. Most of themare nonlinear vibration in the engineering practice. Vibration includes numerousnonlinear factors, resulting in different and unique method for analysis. In thispaper, according to the mathematical models, general analysis of nonlinearvibration was performed to investigate the characteristics and stabilities of thehysteretic system and fluid-structure coupling system.In view of the nonlinear hysteretic vibration system, the differentialequations of the two DOFs wire cable isolator are established under the basicexcitation. Using the Fourier series expansion method and the Harmonic balancemethod，the corresponding frequency response equations of the mass, damping,stiffness, and hysteristics are derived. Then, their numerical solution is got bythe MATLAB. Under the harmonic force, the corresponding frequency responsecurves are got by ABAQUS. The influences of physical parameters of wire cableisolator on the frequency response were analyzed.In the aspect of fluid structure interaction system, dynamic equations ofliquid filled cylindrical shell with different GDOFs under external pressure werederived based on the Donnell shallow shell large theory. The nonlinearproperties were studied by employing the Galerkin and Rung-Kuta methods. Chaos and bifurcation are two typical phenomenons in nonlinear dynamicsystem. In this section, the differential equation of a single DOF wire cableisolator is established under harmonic excitation, and the range of chaos wascalculated by the Melnikov approach. Further, the phase plane, the timedisplacement curve，bifurcation diagram and safe basin were captured in thisrange. Meanwhile, the investigation was executed about the effects of fivecontrolling parameters-linear stiffness, nonlinear stiffness, damping, excitationforce and frequency-on the chaos phenomenon. |
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