Nonlinear Dynamic Analysis And Vibration Control Of Quasi-zero Stiffness Isolator

The quasi-zero-stiffness isolator is paralleled by positive and negative stiffness,which makes the stiffness of the system does to the static equilibrium position close to zero.By reasonably optimizing the geometric stiffness parameters of the structure with negative stiffness,the vibration isolator system has both large bearing capacity and superior low frequency vibration isolation performance.Therefore,the research on quasi-zero-stiffness isolator has become a hot topic in the dynamics,vibration and control field.In view of the unclear understanding of the special dynamical phenomena and mechanism of the quasi-zero-stiffness isolator and the multistability control at present,the local dynamics and global dynamics of two types of quasi-zero-stiffness isolators are deeply studied in this paper.The local dynamical bifurcation phenomenon of the system with bursting oscillation mode is revealed.A novel global dynamical phenomenon of basin of attraction is discovered.Two effective multistability control methods are proposed.The main contents of this paper are arranged as follows:Combining parallelly the negative stiffness magnetic springs with the linear positive stiffness springs,a novel quasi-zero-stiffness vibration isolation system was designed.By analying the characteristics of force-displacement structure and stiffness-displacement structure,the conditions with quasi-zero-stiffness are obtained.Using the method of numerical calculation,the complex nonlinear bursting oscillation forms of the system is revealed,and a novel unconventional bifurcation behavior is found.The periodic bursting oscillation and chaotic bursting oscillation alternate repeatedly due to multiple tangent bifurcation.The periodic bursting oscillations repeatedly occur transcritical bifurcation.This phenomenon shows that the dynamical bifurcation behaviors of this novel magnetic quasi-zero-stiffness isolator are sensitive to the system parameters.The change of the external excitation frequency will cause the system to generate different forms of bursting oscillation.The global dynamics are studied and a novel Wada basin structure is found in a class of nonlinear quasi-zero-stiffness isolator.At present,the number of Wada basin of nonlinear systems is no more than five.In this paper,it is found that the system can have twenty-six Wada basins.By using the method of topological dynamical system,it is proved that all the basins of attraction are Wada basins.These Wada basins are analyzed by using the order theory of saddle and the Wada number,revealing the organization regular of all basins of the system.It is also described their hierarchical nested structure and rotational structure.The problem of multistability vibration control of a quasi-zero-stiffness isolator is studied.Multistability control with complex basin structure is proposed.Two effective control methods including external drive control and piecewise damping control are proposed for the multistable attractor with complex boundaries.The chaotic vibration(harmful vibration) with Wada basin structure is realized by the external driving control method.By means of piecewise damping control method,unnecessary vibration states are effectively controlled.