Research On Dynamics And Vibration Control Based Upon High-performance Low-frequency Isolator

With the developments of the science and technology in recent years, the demands for the protections of the major engineering constructions, structural installations and sensitive instruments from impacts, random vibrations, seismic waves, and so on, are becoming high and pressing, which requires to accelerate the development of high-performance vibration isolators. As well known, the linear isolators are only useful if their natural frequencies are well below the excitation frequency. Hence, it is imperative to propose new types of nonlinear isolators such as low-frequency isolators and to improve their performance in terms of the theories of nonlinear dynamics and vibration control.Aiming at improving the performance of low-frequency isolators, this study provides new insights into the complicated nonlinear dynamics of a mathematical model for a geometric nonlinear quasi-zero-stiffness isolator, and proposes the related theories and methods of achieving the vibration isolation and impact protection. The major research contents and achievements can be summarized as follows:Firstly, the mathematical model is constructed for a quasi-zero-stiffness oscillator,which is composed of a lumped mass connected with a vertical spring of positive stiffness and a pair of horizontally compressed springs providing negative stiffness, which can achieve the quasi-zero stiffness widely used in vibration isolation. The local and global bifurcation analyses are implemented to reveal the complex dynamic phenomena of this system. The double-parameter bifurcation diagrams are constructed to demonstrate the overall topological structures for the distribution of various responses in parameter spaces. Using the Floquet theory and parameter continuation method, the local bifurcation patterns of periodic solutions are obtained. Moreover, the global bifurcation mechanisms for the crises of chaos and metamorphoses of basin boundaries are examined by analyzing the attractors and attraction basins, exploring the evolutions of invariant manifolds and constructing the basin cells. Meanwhile, additional nonlinear dynamic phenomena and characteristics closely related to the bifurcations are discussed including the resonant tongues, jump phenomena, amplitude-frequency responses, chaotic seas, transient chaos,chaotic saddles, and so on, and also their generation mechanisms are presented.Secondly, the proposed quasi-zero-stiffness isolator subjected to the harmonic forcing and base vibrating excitations is investigated for the characteristics of vibration isolation. This study considers the prototypical system with the irrational nonlinear restoring force instead of the conventionally approximate Duffing system, which can provide the precision results unquestionably especially for the prediction of a large displacement behavior. The characteristics of amplitude-frequency response and transmissibility of the model are derived by using an extended averaging approach, and meanwhile the process of parameter optimization is proposed for the maximum low-frequency band of isolation.Furthermore, the numerical simulations are carried out to verify the analytical results and to reveal the complex dynamical phenomena such as the coexistence of multiple solutions. Based upon the analysis of attractor-basin portraits, the control idea by choosing the initial value to obtain the desired small amplitude and to avoid the other coexisted solutions is proposed.Thirdly, a piecewise damping control method is proposed to improve the performance of the quasi-zero-stiffness isolator. The new control policy is achieved through switching the damping of isolator between the soft- and hard- modes that depend on a preset value of relative displacement(PRD). This control approach can largely lower the isolation frequency while enhancing the effectiveness of isolation in high frequencies and preventing the severity of end-stop impacts. To realize such control objective, two key issues are solved including the suppressing of period-3 solutions that co-exist with the desired period-1 orbits and the optimization of PRDs based upon the analysis of twoparameter bifurcations and basins of attraction. Finally, the capability of the proposed system in end-stop impact protection is studied, which shows that it can successfully prevent the impact and quickly stabilize the large-amplitude response into the ideal steadystate motion.