Structural Design And Vibration Isolation Characteristics Analysis Of Nonlinear X-shaped Quasi-Zero-Stiffness Vibration Isolator

Vibration is a double-edged sword,but in most engineering fields,vibration is considered negative.It is impossible to eliminate the vibration in practical engineering.At present,the most direct and effective method to reduce the transmission of vibration to the target object is vibration isolation.The passive vibration isolation technology has the advantages of convenient implementation,low cost and high reliability,which is more desirable in practical application.In this paper,the vibration isolation system of X-shaped(i.e.spring and damper arranged in X-shaped)is taken as the research object,and the structure is completely designed independently.It includes:X-shaped quasi zero stiffness vibration isolator and double-layer X-shaped vibration isolation system;Lagrange equation,Taylor approximation expansion,incremental harmonic balance(IHB)method and Floquet theory were used to solve the dynamic modeling,The nonlinear vibration and low frequency vibration isolation characteristics of the two self-designed vibration isolation systems are studied in depth.The main contents of this paper are as follows:(1)An X-shaped structure is applied to the design of vibration isolator.Based on the force analysis of X-shaped structure,the dynamic equation of the system is established,and the nonlinear ordinary differential equation is solved by the incremental harmonic balance method and the arc-length increment method.The influence of equivalent reduced stiffness γon the system transmissibility(force transmissibility and displacement transmissibility)is discussed in detail.The results show that the equivalent reduced stiffness γ value of X-shaped quasi-zero-stiffness(QZS)isolator is an ideal parameter which can effectively reflect the lowfrequency vibration isolation effect of the system.(2)The nonlinear resonance of double-layer X-shaped vibration isolation system is studied.Considering the vertical and rotational displacements of the upper and lower platforms,the nonlinear dynamic model of a four degree-of-freedom structure is established by using Lagrange equation.The steady-state amplitude frequency response of the system is obtained by using the(IHB)method,and verified by Runge-Kutta numerical simulation.The effects of excitation amplitude,damping coefficient,mass ratio of upper and lower platforms,stiffness ratio and light rod length on the nonlinear vibration response of double-layer Xshaped vibration isolation system are analyzed.Interestingly,the double-circle resonance curve is found when analyzing the influence of the platform length on the nonlinear vibration response of the system.(3)The low-frequency vibration isolation performance of double-layer X-shaped vibration isolation system is studied.The vibration isolation performance of the double-layer X-shaped vibration isolation system is evaluated by using the peak value of the force transmissibility and the vibration isolation bandwidth.The effects of excitation amplitude,damping coefficient,mass ratio of upper and lower platforms,stiffness ratio and light rod length on the isolation performance of nonlinear vibration isolation system are discussed in detail through numerical examples.(4)The force transmissibility of double-layer X-shaped vibration isolation system is studied by experiment.Because the double-layer X-shaped vibration isolation system has good vibration isolation performance,the double-layer X-shaped vibration isolation system is designed and manufactured,and the experimental equipment of the double-layer X-shaped vibration isolation system is established.Under the action of different harmonic excitation,the force transmissibility characteristic data of double-layer X-shaped vibration isolation system are obtained,which verifies the correctness of the simulation results.