Dynamic Analysis Of A2DOF Nonlinear Vibration Isolation System And Time Delay Control

Vibration isolation is the most frequently used approach to isolate the machineryvibration from transmitting to the submarine. According to the broad spectra feature ofchaos, chaotification of the nonlinear vibration isolation system is employed to reducethe line spectra of the submarine, in order to enchance its stealth capability. In thisdissertation，two aspects of research are conducted. The nonlinear dynamic behaviorof the2degree of freedom (dof) nonlinear vibration isolation system is studed. Basedon the idea of reducing the line spectrum by chaotification, one challenge is how toprovoke chaos and maintain chaos. Another hinder is that how to induce chaos withtiny energy. In order to cope with these difficulties, several control methods areempoyed in the dissertation. The research results are significant not only in theacademic but also in the practical engineering. The main results contain as follows.By simplifing the three dimensional vibration isolation model into onedimentional beam, adopting the Euler-Bounuli hipotheis, and considering thegeometric nonlinearity, the static and dynamic behavior of the two layer beamscoupled by nonlinear isolators are investigated. The Differential-Quadrature methodand Galerkin method are employed to convert the partial differential motion equationsinto differential equation with respect to time. By Nermark or Longe-Kutta method,the differential equaiton can be integrated numerically. The static deformation of thebeams are compared with the results obtained by comercial software ANSYS.The two-layer vibration isolation system is further simplifed into a2-dofmass-spring system. The passive vibration isolation approach is adopted byintroducing floating raft and nonlinear isolators. The linear feedback control is alsoimplemented to the vibration isolation system. The approximate solution of thenonlinear vibration isolation system is obtained by average method and the nonlineardynamic behavior is studied. According to numerical simulation, the effect of systemparameters on the dynamic behavior of the system is discussed. The bifucationdiagrams show the viaraiotn of the system motion states with respect to the excitingfrequency and control gain.The generalized chaotic synchorization method is employed by using theresponse of the Lorenz system family, such as Lorenz system, Chen system, Lü system,R ssler system and Chua system, as driving signal. When the drive system is set tohaving chaotic attrators, the chaotic signal is used to synchorize the vibration isolationsystem to be chaotic. The Hooke-Jeeves optimazation method and implicit index function are used to optimize the control gain in order to obtain chaos with betterquality. By numerical simulation, the dynamic behavior of the vibraiton isolationsystem is studied and the chaotification effect of the Lorenz system family isinvestigated.The time delay can make the vibration isolation system have infinite dimension,which makes the ease of chaotification. The nonlinear vibration isolation system islinearized at the equilibrium point and the characteristic equation is obtained byLaplace transformation. Due to the time delay, the characteristic eqation is atranscendental equation, which has infinite eigenvalues, that is, the infinite dimensionof the time delay system. As for the time delay system, the stability of the sytem isassociated with time delay. The general strum criterion is adopted to predicte thedistribution of the roots. Then the critical control gain for the delay-independentstaiblity is obtained and the critical time delays for the stability change are studied.The numerical cases are investigated to verify the correctness of the theoreticalconclusion.Assuming the vibration isolation has small damping, small control gain and smallexciting amplitude, the multiscale method is used to obtain the approximate solutionof the nonlinear vibration isolation system under primary and1:1resonance. Theaverage equation involving time delay is obtained. By investigating the equilibriumsolution and the stabilty, the effect of system paramters and time delay controlparameters on the dynamic behavior of the system is studied. The results show that byadjusting the control parameters the vibraiton amplitude of the system can becontrolled. The vibration amplitude is changed with increase of time delay. Thereforethe system paramters can be tuned to reduce the vibration amplitude. The stability ofthe system also depends on the time delay control setting. With comparison withbifurcation diagram, the unstable region corresponds to chaotic region correctly.Stability of the sytem with dual time delay control is studied. When the dual timedelay control has the same delay, the generalized strum method can be used. Whenthey are unequal, the quadratic eigenvalue method is adopted. By matrix and operatorcomputation the eigenvalue of the characteristic equaiton and critical time delay areobtained. The delay-independent stability region is obtained and the critical time delayof stability change is attained. Effects of different control parameter, control scheme on chaotification of the vibraiton isolation system are investigated. The stabilityregion and chaotification effect of single time delay and dual time delay are compared.