Power Flow Analysis On Nonlinear Vibration Isolation System

Passive vibration isolation has become the first choice for vibration control of aerospace engineering because of its simple structure and strong economy.The nonlinear stiffness isolation system has low dynamic stiffness and small static deformation,which is one of the current research hotspots.In addition,the nonlinear damping can effectively suppress the resonance response,and it will not deteriorate the vibration isolation effect of the resonance response.The current outstanding problem is that there is a strong coupling between the isolator and the foundation.Previous studies based on the basic rigidity assumption will lead to deviations in the evaluation of vibration isolation.This paper aims to introduce power flow to design nonlinear stiffness and nonlinear vibration isolation.Nonlinear damping and nonlinear stiffness vibration isolation characteristics are studied.Firstly,nonlinear damping is introduced to strengthen the double-layer nonlinear vibration isolation system with high static and low dynamic stiffness.Horizontal springs provide negative stiffness that allows the vibration isolation system to have high-static-low-dynamic-stiffness characteristics,and horizontal damping provides the nonlinear damping of the system.The dynamic equations of the two-stage nonlinear vibration isolation system are established.The system's amplitude-frequency response equation is given based on the harmonic balance method.The system response curve is obtained and verified by numerical simulation.The linear damping and nonlinear damping of the system are compared.The influence of the vibration isolation system,the influence of the system parameters on the vibration isolation was studied.As a result,it was found that the nonlinear damping suppresses the resonance with respect to the linear damping without affecting the vibration isolation effect in other frequency ranges of the system.The power flow characteristics of a single-stage and two-stage vibration isolation system with nonlinear stiffness and nonlinear damping under displacement excitation are studied.The power flow of strong nonlinear vibration of the system is analyzed by harmonic balance method.The influence of nonlinear stiffness and nonlinear damping on the power flow is discussed.The research shows that the nonlinear stiffness of single-stage vibration isolation system can broaden the isolation frequency band,and the nonlinear damping can maintain high-frequency vibration isolation performance.The nonlinear stiffness of each stage in the two-stage vibration isolation system can effectively extend the isolation frequency band and reduce the power flow rate at high frequency.The introduction of the nonlinear damping in each stage can reduce the first response peak value and get better isolation effect.The power flow characteristics of a single-stage and two-stage vibration isolation system with nonlinear stiffness and nonlinear damping under force excitation are studied.The dynamic model of the foundation-nonlinear vibration isolator is established.The amplitude frequency response equation of the system is obtained by the harmonic balance method,and the input power,transmitted power,power transmissibility and the force transmissibility are derived,and the response curves are verified by the numerically.The influence of nonlinear stiffness and nonlinear damping on the power flow and force transmissibility of single and two-stage nonlinear vibration isolation system is discussed.It is found that the nonlinear stiffness can broaden the isolation frequency band,and the nonlinear damping can restrain the first resonance and does not affect the isolation effect of other frequencies.An integrated nonlinear vibration isolation and energy harvesting model based on bi-stable composite plates is proposed.In this model,the bi-stable composite plate provides negative stiffness and nonlinear stiffness in the system.At the same time,piezoelectric is bonded on the bi-stable composite plate to collect the energy generated in the vibration.The force displacement curve of the bi-stable composite plate is obtained through static analysis.Based on this,the system dynamics equation and the piezoelectric coupling equation are established,and the harmonic balance method is used to calculate the dynamic equations and piezoelectric coupling equations.The procedures of derivation are presented and the correctness of the asymptotic treatments is validated by numerical simulation.The nonlinear characteristics of the efficiency of vibration mitigation is subsequently evaluated by force transmissibility and harvesting voltage.The maximum generated voltage is 3.8V,the reduction of the force transmissibility is 23 d B when bi-stable composite plate is used.