Investigations On Passive Vibration Control Based On Periodic Structure And Quasi-zero-stiffness

With the development of the times and the continuous innovation of science technology,the vibration control becomes more and more important in various engineering fields.Nowadays,there have been many mature theories and methods of vibration control,such as active control,passive control and semi-active control.Active control can obtain a good control effect in the theoretical research,but it is difficult to apply for the case of the engineering environment.The passive control has the advantages of good adaptability,strong feasibility and low environmental requirements,which is the mainstream of the design and application of vibration reduction and isolation.In the research of vibration reduction,the study of periodic structure has been attracting much attention.The band-gap characteristic of these structures can attenuate the elastic wave propagation and achieve the vibration reduction,and this characteristic provides an effective reference for passive vibration control.Two periodic structures are designed and investigated,and their vibration band-gap characteristics are also optimized to improve the vibration reduction effect.In the research of vibration isolation,the quasi-zero-stiffness(QZS)vibration isolation systems have received much attention in the field of ultra-low frequency vibration isolation because of low starting vibration isolation frequency and small resonance peak.A quasi-zero-stiffness vibration isolation system with additional X-shaped structure(X-QZS)is studied.By adjusting the parameters,this system not only has a wide QZS interval and a low starting vibration isolation frequency but also a good load carrying capacity.Based on the two previous studies,a locally resonant beam with quasi-zero-stiffness supports is proposed,and the vibration reduction and isolation characteristics are analysed.The main works of this article are as follows:A hierarchical periodic beam is designed and researched,and the locally resonant and Bragg scattering mechanism are combined to improve its vibration band-gap characteristics.The dynamic model of the hierarchical periodic beam is built and the dynamic responses are calculated using spectral element method(SEM),and the attenuation constants are solved by the transfer matrix method(TMM).The results are verified by vibration experiment and finite element method(FEM),and the effects of the number of unit-cell and the structural parameters in the subperiod on the vibration band-gap characteristics are discussed.The results show that changing the parameters of L-shaped components can better improve the band-gap characteristics.Among these,as the thickness of the vertical component increases,the number and width of the band-gaps increase significantly.A kind of periodic metamaterial plate is studied to obtain the vibration band-gap characteristics in the low frequency range.Based on the Floquet-Bloch theory,the FEM is used to build the model and calculate the band structure.The calculation results are verified by SEM and vibration experiment,and the vibration band-gap characteristics of the structure are analyzed.In addition,the effects of the structural and material parameters on the vibration band-gap characteristics are investigated.It can be found that the existence of the outer membrane can broaden the band-gap well,and the material and radius of the mass hemisphere can affect the upper and lower boundaries of the band-gap respectively,and widen the band-gap from different directions well.Through asymptotic optimization,the periodic beam and plate structure are optimized separately in different optimization target and the performances of vibration reduction on specific frequency ranges are improved.With the attenuation constant as the optimization basis,the band-gap ratio of the hierarchical periodic beam in 0-2000Hz is optimized,and the vibration band-gap characteristics in this frequency range are greatly improved,then the correctness and feasibility of the optimization are verified by the vibration experiment;Based on the band structure,the vibration reduction performance of periodic metamaterial plate is optimized in the 40-70Hz frequency range,and the band-gap is widened while the target band-gap position is achieved.A quasi-zero-stiffness vibration isolation system with additional X-shaped structure is designed and studied,and a wide QZS displacement interval and a low starting vibration isolation frequency are obtained,and the load carrying capacity is improved in a certain extent.The effect of the structural parameters on the system stiffness is investigated by statics analysis.The amplitude-frequency characteristic curves and the force transmissibility are calculated by the harmonic balance method(HBM),and the vibration isolation properties are analyzed using four vibration isolation performance indexes.And the nonlinear dynamics are analyzed by parametric excitation.The damping of the experimental prototype is estimated by the vibration experiment,and the correctness of the calculation results and the design feasibility are also verified.In the experiment the obvious nonlinear jump-down phenomenon appears,and the jump-down frequency agrees well.The study shows that the vibration isolation system has a good ultra-low frequency vibration isolation performance.A locally resonant beam with quasi-zero-stiffness supports is proposed.The influences of the vibration isolator and the vibration isolation system parameters on the vibration reduction and isolation characteristics are analyzed.The dynamic model is built and the dynamic response and transmissibility are calculated by HBM,and the results are verified by numerical method.The research shows that the locally resonant beam with quasi-zero-stiffness supports can combine the vibration reduction and isolation characteristics to achieve a good passive vibration control performance.