Structure Optimization And Mechanism Research On Targeted Energy Transfer Of Nonlinear Energy Sink

Most of the phenomena in nature are involved in the transmission of energy in some form.Based on the target energy transfer phenomenon in nonlinear mechanical structures,the related structures and models are proposed and studied for their dynamic characteristics and vibration suppression efficiency.The main research contents are as follows:(1)Mechanism study of target energy transfer.Firstly,the internal resonance characteristics of the undamped free-vibration cubic energy sink(NES)system are analyzed based on the averaging method.The frequency energy curve under 1:1 internal resonance is derived,and the dependence of the frequency and energy of the vibration system is revealed and the target is pointed out.The damping condition of the energy transfer cannot be greater than the critical damping given.At the same time,the vibration mechanism of cubic NES under single-frequency excitation is studied,and the dynamic characteristics are similar to those of free-vibration system.The damping condition for generating target energy transfer can not be greater than the critical damping given by the first-order scale slowly varying equation.Stability analysis,we conclude that SMR appears in the amplitude point jump region of the system equilibrium point,and gives the two critical points where the excitation force satisfies the amplitude jump.The system experiences a slow variable amplitude quasiperiod.In the response domain,the linear optimal dynamic vibration absorber is used as a comparison.The vibration efficiency of the vibration system is measured by the energy criterion of the whole vibration process of the system.We compare the vibration energy suppression efficiency of the two at different frequencies.In the SMR interval,the efficiency of the nonlinear energy sink changes with the parameters such as nonlinear stiffness,and the efficiency also changes significantly.The higher the nonlinear stiffness,the higher the vibration suppression efficiency.However,the nonlinear stiffness exceeds the critical point,which causes the system to jump out.The interval is varied,resulting in an increase in vibration suppression efficiency.(2)Optimization of target energy transfer.Based on the complex averaging method,the invariant manifolds and integral invariants of slowly varying amplitudes are derived.According to the integral invariants,the critical conditions for the complete energy transfer of the system are obtained.According to the characteristics of the target energy transfer,the critical condition is Produce optimal target energy transfer.The energy of the optimal target energy transfer is dependent on the nonlinear stiffness.When the energy is not satisfied,the passive energy sink will be separated from the optimal target energy transfer due to the 1:1 transient resonance capture.Based on the analytical derivation of nonlinear stiffness,the optimal governing equation is established,so that the nonlinear stiffness maintains the dependence of energy,and the optimal control equation is optimized by the variation of the integral invariant in the presence of damping.It shows that the designed strategy effectively improves the vibration suppression efficiency of optimal target energy transfer.Finally,the optimal target energy transfer of the beam is studied.The first-order scale equation of the invariant manifold is established based on the complex averaging method.It is pointed out that its characteristics are similar to the single-degree-of-freedom system.The vibration,the additional energy sink position is lower at the ends of the beam and the middle,and the efficiency is the highest when the energy sink is located at the middle of the two sides,and the nonlinear stiffness also has a critical value,that is,the nonlinear stiffness exceeds the threshold.The target energy transfer phenomenon is triggered at the moment,and the optimal target energy transfer is achieved at the threshold,and the EDM slowly decreases as the nonlinear stiffness is further increased.Based on the analysis of the problem of the tensile support at both ends of the thin steel sheet,it is pointed out that the restoring force generated by the linear stiffness is weaker and negligible than the nonlinear stiffness.We use two thin steel sheets symmetrically arranged and vertically from the middle.The direction stiffness is used to realize the cubic stiffness energy sink and attached to the beam.The vibration of the beam is experimentally studied.The results show that the free vibration of the beam after the additional NES is quickly suppressed,and the vibration suppression effect of the NES installation position on the beam is summarized.(3)Vibro-Impact energy sink.Firstly,the time scale of the Vibro-Impact system studied is transformed by sawtooth wave,and the dynamic differential equation based on sawtooth time is established.Due to the strong nonlinear characteristics of the Vibro-Impact,it is similar to the cubic stiffness nonlinearity in the previous study.There is no linear natural frequency.From the structure of the diagram,it can be seen that the vibration is completely dependent on the Vibro-Impact with LO.Under suitable parameters,the Vibro-Impact energy can achieve 1:1 internal resonance capture in a short time scale,keep the same frequency oscillation with LO and quickly consume the system vibration energy to achieve target energy transfer.Under the premise of 1:1 resonance,the analytical expression of the zero-order scale of the system is obtained based on multi-scale expansion,and the analytical relationship between the system’s slowly varying amplitude and Vibro-Impact recovery coefficient and Vibro-Impact gap is obtained according to the Vibro-Impact condition,and the optimal gap is derived.Expression.The numerical results show that the Vibro-Impact energy sink can absorb the vibration energy of the system quickly under the appropriate Vibro-Impact gap,and has better vibration suppression effect.As the energy of the system decreases,the energy sink slowly oscillates after the energy leaves the resonance capture zone.(4)Optimization and improvement of nonlinear energy sinks.In view of the problem that the sensitivity of the energy sink to the input energy leads to the decrease of efficiency,three improved energy sink structures are proposed,namely the multi-degree-of-freedom stiffness uniform energy sink,the parallel energy sink of the cubic array Vibro-Impact matrix and the energy of the cubic Vibro-Impact energy sink.Based on the inverse correlation between nonlinear stiffness and energy of the optimal target energy transfer,we propose an energy sink with uniform nonlinear stiffness to improve the efficiency of target energy transfer.The Vibro-Impact motion can change the amplitude and frequency of the energy sink vibration by adjusting the Vibro-Impact gap,and has the characteristics of rapid response,but the optimal efficiency is lower than that of the cubic oscillator.Therefore,the impact vibrator can work in conjunction with the cubic vibrator.When the pulse excitation is lower,and the target energy transfer does not occur in the cubic energy sink,the introduction of the Vibro-Impact can trigger the target energy transfer phenomenon.Under the optimal target energy energy transfer state,the Vibro-Impact can improve the NES vibration suppression efficiency to some extent,and the experimental structure is designed to study the energy sink of the cubic Vibro-Impact.The results show that the efficiency of target energy transfer is greatly improved by the optimized structure proposed in this paper.