Study On Dynamics Characteristic Of 2-D Gyroscopic Phnonic Crystals

Vibration is a kind of motion that exists widely in nature.It transmits in the form of wave in structure or medium.In practical engineering structures,vibration will occur due to the accuracy of parts processing or wear problems.Vibration accelerates wear and tear of parts in engineering structures,and severe vibration can also lead to structural damage,resulting in hidden safety hazards and economic losses.Therefore,how to control the vibration precession has always been the focus of Engineering research.Phononic crystal is an artificial periodic structure.For its band gap characteristics,the vibration of frequency in the band gap can be suppressed,and it has attracted wide attention.Vibration is classified according to displacement characteristics as bending vibration,torsional vibration and stretching vibration.Based on the characteristics of gyroscope,in this paper,a new phononic crystal model of gyroscope is proposed.It mainly studies on the characteristic of torsional vibration,in this model,and how to control it in the structure.The main contents of the paper are divided into three parts:(1)Based on the angular momentum theorem and some basic assumptions,the dynamics model of the quadrilateral array of gyro phononic crystals is established,and the dispersion relationship is obtained by the Bloch theorem.Some critical parameters of the system,such as angular momentum,moment of inertia and torsional stiffness,are studied to analyze the development of band structure so that bandgap is proved theoretically.Moreover,the effect of vibration suppression has been verified by numerical simulation results.(2)It found that two dispersion surfaces in band structure are corresponded to different directions of wave by studying the dynamic response characteristic under excitation in different band structures,positive rotating wave and reverse wave respectively.Only one wave will be allowed to pass in the structure with band gap,and two waves can be allowed to pass simultaneously,however,in the structure with overlapped passband.The trajectory of gyroscopes,in the structure with band gap,is only circular,while it has both circular and linear trajectories in the overlapping passband structure.(3)Based on the dispersion relation,the propagation direction and velocity of waves are theoretically analyzed,and the propagation characteristics of waves in structures are studied.The theoretical results show that the propagation direction of the wave is consistent with the normal direction of the contour of the dispersion surface,and the velocity in this direction is determined by the intersection point of the group velocity contour and the frequency contour.Then the correctness of the theoretical analysis is verified by the numerical simulation results.Finally,combined with the previous analysis,using the structural characteristics of phononic crystals to achieve the control of wave propagation range and angle.