Research On Dynamic Characteristics Of Phononic Crystals With Locally Resonant Structures Based On Non-smooth System

Low-frequency vibration and noise not only seriously affect human health,but also have adverse effects in the fields of transportation,aerospace and precision machining,resulting in a large number of economic losses.Especially the low frequency vibration of less than 600 Hz is the main threat at present.The application and research of phononic crystal(Phononic Crystals)broadens the way for vibration and noise reduction technology,especially for phononic crystals designed based on local resonance mechanism,and its sub-wavelength elastic wave / acoustic wave regulation mechanism provides a new idea for low frequency vibration and noise reduction.Phononic crystals refer to the materials or structures with periodic distribution of elastic constants and density.The local resonance structure is the most representative,and its elastic wave band gaps can effectively restrain the low frequency vibration of the structure.The application of linear phononic crystals is limited because it is difficult to suppress low-frequency and wide-band vibration at the same time.Therefore,in this paper,the nonlinear effect is introduced on the basis of linear phononic crystals,and the action mechanism of nonlinear mechanism on low frequency band gap is studied.In this paper,the formation mechanism of nonlinear phononic crystal band gap structure under the action of nonlinear mechanism is analyzed by means of numerical simulation and experimental verification.Based on the theory of one-dimensional locally resonant phononic crystals,the nonlinear phononic crystal structure is constructed by introducing nonlinear effect on the basis of linear locally resonant phononic crystals.The dynamic characteristics of nonlinear locally resonant phononic crystals and the action mechanism of the unit cell of the non-smooth collision system on the chaotic band gaps are studied.The details are as follows:(1)Study of nonlinear locally resonant phononic crystals based on torsional vibration.The energy band structure of torsional vibration of one-dimensional locally resonant phononic crystals is calculated by transfer matrix method and MATLB.By changing the structure parameters,the influence of structure change on the upper and lower bounds of band gaps range is analyzed,and the band gaps variation law and band gap regulation mechanism are studied and compared with the experimental results.Then,using the single-degree-of-freedom vibration collision theory,the nonlinear dynamic behavior of the unit cell is analyzed by MATLAB numerical calculation,and the frequency range of chaotic band gaps in the system is clarified,which is verified by experiments.On the one hand,in a specific frequency range,each unit cell resonates and couples with the torsional waves between the axes,which can open multiple linear resonance band gaps in the low frequency range.On the other hand,the nonsmooth system based on collision mechanism will bring nonlinear dynamic characteristics to the oscillator and produce chaotic band gaps in the low frequency range.The research results show that the structure not only has obvious vibration suppression effect in multiple frequency ranges under linear characteristics,but also its chaotic characteristics can broaden the band gaps range to achieve vibration reduction characteristics.(2)Study on nonlinear locally resonant phononic crystals of composite cantilever structure.Based on the exploration of the mechanism of low frequency broadband vibration suppression,a strongly nonlinear phononic crystal structure is designed,and the nonlinear vibration characteristics,chaotic response and bifurcation laws in different frequency bands are studied based on numerical simulation and experiments.carry out mechanism verification and study its application of low frequency broadband vibration reduction.Firstly,the vibration collision system of single-degree-of-freedom cantilever beam is studied by experiments.The excitation frequency is changed many times under the basic excitation,and the measured response is analyzed and processed in frequency domain by MATLAB software,and many kinds of nonlinear dynamic phenomena such as complex period,almost period,chaos and so on are observed,which provides a method for the follow-up analysis and application of chaotic motion.The linear phononic crystals structure of the finite element is simulated by COMSOL numerical simulation.The bridging coupling phenomenon was observed in the experiment,and the chaotic band effectively bridged the two bandgaps separated by the passband generated by the formant.The amplitude intensity in the chaotic bandgaps attenuates violently,which effectively suppresses the resonance peak of the linear oscillator in the finite structure passband due to the local resonance phonon crystal structure,and clarifies the bandgaps control mechanism.the improvement of vibration suppression performance of local resonance phononic crystal structure by nonlinear effect is verified.