Modeling And Analysis Of A Pendulum-like Vibration Isolator With High Static And Low Dynamic Stiffness

Vibration is a common phenomenon in nature.With the unprecedented progress of science and technology in the world,higher and higher requirements are made on the operation status and environment in engineering.More and more tiny instruments are used in engineering projects.However,it is known that these instruments are very sensitive to low-frequency vibration,and traditional linear vibration isolators are not capable of isolating these low-frequency vibration due to the trade-off between stiffness and stability.Due to the character,lower dynamic stiffness with higher static stiffness,spring mechanism with the combination of positive and negative stiffness owns,many researchers have studied this low dynamic and high static vibration isolation structure to break the limitation of traditional vibration isolation,and they have made big breakthroughs in the field of HSLD recently.However,most of the systems studied so far are geometrically nonlinear systems with hard stiffness.Compared with the geometrically nonlinear systems with soft stiffness,the hard nonlinearity will reduce the range of vibration isolation due to the existence of jump phenomenon.In order to weaken the impact of hard nonlinearity,a pendulum-like HSLD isolator is designed in this paper.The purpose is to weaken the the influence of hard nonlinearity by gravity pendulum element to expand the range of vibration isolation.The main contents of this paper are as follows:Based on the basic quasi-zero stiffness three-spring model,a new stable quasi-zero stiffness vibration isolator is designed by introducing an element of gravity pendulum.The purpose is to weaken the hard impact of the original three-spring model by the soft nonlinearity of the gravity pendulum.The model of the new designed vibration isolator is established,the relevant system parameters are given,the dynamic equation of the system is deduced,and the equilibrium points of the system are explored.Static analysis of the system is investigated.The paper firstly studies the discontinuity of the system and its consequences.And then,the restoring force,stiffness of the lumped mass and the restoring moment of the rigid bar are deduced.The stable quasi-zero stiffness characteristics of the system are proved.The relationship of parameters under the condition of obtaining quasi-zero stiffness are given.The stability of the system under different stiffness ratios is calculated,and the optimum stiffness ratio is given when the geometric parameters are fixed.Two methods,numerical simulation and theoretical solution,are used to solve the new designed vibration isolator.The response curves and phase curves of the system under different excitation frequencies are analyzed.The nonlinear characteristics of the system are explored,and the effects of different parameters on the nonlinear characteristics of the system are analyzed.Comparision is made with the traditional linear passive vibration isolator and the basic three-spring nonlinear vibration isolator.The amplitude-frequency response curves and transmisibilities of these systems are studied and compared.The results show that the new designed vibration isolator a SQZS system,and the skeleton curve of its amplitude-frequency curve bends to the left,showing obvious soft nonlinearity.Due to the existence of jumping phenomenon,the new vibration isolator can expand the vibration isolation range of the previous system to a certain extent and improve the effect of low-frequency vibration isolation compared with hard nonlinear vibration isolation and traditional linear passive vibration isolation.Thus,it has certain value.Finally,the research of pendulum isolator with low dynamic and high static performance is prospected.