Investigation On Dynamic Behavior Of Nonlinear Vibration Isolation System

Introducing an isolation mount between a source and a receiver is the most commonly adopted solution to reduce the level of transmitted vibrations.However,linear single-stage vibration isolation systems have a limitation on their performance,which can be overcome passively by using linear two-stage isolation systems.It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by introducing negative stiffness structure,to achieve a low dynamic stiffness and hence low natural frequency,but at the same time having a low static deflection.In this paper,an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation.The dynamic of the bi-stable system which is composed of negative stiffness and mass is investigated.When excitation of harmonic force without noise perturbation,at small amplitude,it is found that the system is constrained to vibration in one of the well and behave as soften nonlinearity even the coefficient of the cubic term is positive.At large amplitude,the system jump between the two-wells,chaotic motion occurs,the attractor basin is characterized by cell-to-cell mapping method.When excitation of harmonic force with noise perturbation,it is clear that instead of making the system disorder,putting in moderate noise can improve the ratio of signal to noise(SNR)of output force.In further,the explanation for this phenomenon is given.It is approved by the experiment results which rig is composed of two magnets and a cantilever beam.Nonlinear single-stage isolation system is achieved by the two additional horizontal springs(negative stiffness structure)placed onto spring-mass-damper system.The force transmissibility of the nonlinear single-stage isolation system with different horizontal stiffness is concerned.When the horizontal stiffness exceeds the critical stiffness,the system becomes the bi-stable system,and then its isolation performance is investigated under harmonic and random excitation respectively.Compared with mono-stable system,it is found that the optimum performance is achieved by quasi-zero stiffness at both harmonic and random excitation.The most desirable configuration of a two-stage nonlinear vibration isolation system,in which the isolators contain hardening geometric stiffness nonlinearity and linear viscous damping,is investigated.The force transmissibility of the system is used as the measurement of the effectiveness of the isolation system.The hardening nonlinearity is achieved by placing horizontal springs onto the suspended and intermediate masses,which are supported by vertical springs.It is found that nonlinearity in the upper stage has very little effect and thus serves little purpose.The nonlinearity in the lower stage,however,has a profound effect,and can significantly improve the effectiveness of the isolation system.Furthermore,it is found that it is desirable to have high damping in the upper stage and very low damping in the lower stage.An modified two-stage nonlinear vibration isolation system in which the upper horizontal springs are connected to the secondary mass rather than to the ground as was the former desirable configuration case,is investigated.The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied.It is found that there are beneficial effects of using nonlinearity in the stiffness in both upper and lower stages for both types of excitation.Further,it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right,but not the higher resonance frequency.Generally,it is found that a nonlinear two-stage system has superior isolation performance compared to a linear two-stage isolator.A lab-scale two-stage nonlinear isolation system has been designed and consructed.Two bi-stable composite plates were mounted at each stage with four corners clamped and center loading thus had negative stiffness.The force-displacement characteristic of negative stiffness device is measured and compared with analysis results.The other two metal plates provided the positive stiffness and the static load-bearing property.The disturbance source was a harmonic excitation from the base with fixed displacement at each excitation frequecny,the measured transmissibility(RMS of ratio of the upper mass's acceleration to the base's acceleration)was compared with the euqivelent linear isolation system which comprised metal plate only(without two bi-stable composite plates).It is found that the transmissibility is reduced by 25dB at high frequency range by nonlinear isolation.