Optimization Designs And Applications Of Vibration Reduction Control Systems Based On Passive Mechanical Networks And Negative Stiffness Elements

In this thesis,the design of a class of passive vibration systems with a negative stiffness element and an inerter with H_∞optimization criteria is mainly investigated.In practical application,due to the characteristics of simple structure,convenient installation and low cost,passive mechanical control has become the most classic and widely used basic control method in the field of vibration control.The research methodologies and results in this thesis can provide theoretical foundation for the investigations and applications of vibration control systems.The work fulfilled in this thesis is mainly as follows:(1)The parameter optimization design of a novel inerter-based dynamic vibration absorber system with a grounded negative stiffness element is investigated.At first,the frequency response function in the dimensionless form is derived by formulating the system motion equations.Then,since there are four fixed points in the amplitude-frequency response curves of the system,the Extended Fixed Points Technique is adopted to obtain the analytical expressions of the optimal inertance-to-mass ratio,the optimal natural frequency ratio,the optimal corner frequency ratio and the optimal damping ratio of the system in terms of the mass ratio and negative stiffness ratio.Moreover,a necessary and sufficient condition is derived when the parameters are taken the optimal values,by utilizing the Hurwitz stability criterion.At last,compared with other four optimal dynamic vibration absorbers of the similar structure,the novel dynamic vibration absorber system can provide better H_∞performance,and the numerical examples illustrate that the system can provide better time-domain performances under random excitations.(2)The parameter optimization problem of a novel base isolator with a grounded negative stiffness element and an inerter is studied.At first,the motion equations of the base isolation system are established and the transfer function in the dimensionless form is derived.Then,the analytical solutions of the optimal parameter values about the inertance-to-mass ratio,the natural frequency ratio,the corner frequency ratio and the damping ratio in terms of the mass ratio and negative stiffness ratio are derived through the Extended Fixed Points Technique.Moreover,the necessary and sufficient condition for the base isolation system with optimal parameter values to be stable is obtained by the Hurwitz criterion.Finally,compared with other three optimal isolation systems,the optimal isolation system in this thesis can provide better vibration reduction performance.(3)The application research of the base isolation system optimized in this thesis is investigated.The optimal isolator in this thesis and the other three optimal isolators are applied to a four-story building system,and the time domain simulation is carried out under three kinds of actual seismic waves.The displacement response of the top floor of the building,the displacement and acceleration response of the bottom isolation layer under different seismic waves are obtained.It shows that the base isolation system proposed in this thesis has relatively better vibration isolation performance compared with the other three base isolation systems.The optimized results of passive mechanical vibration reduction systems of this thesis can be applied to the design of vibration control systems in practice such as high-rise buildings,industrial liquid storage tanks,bridges,vehicle suspensions,etc and it can provide theoretical basis for the subsequent research of vibration reduction system.