Research On Flexural Wave Dynamic Behavior Based On Crystal Lattice Model

At present,the influence of defects on the propagation behavior of flexural waves is mainly studied by using the theory of continuous model.In this paper,infinite and finite crystal lattice dynamical models are proposed to study the propagation behavior of flexural waves.The propagation characteristics of flexural wave are studied from the perspective of wave.Firstly,we establish a one-dimensional infinite lattice dynamics model with mass defect atoms and local resonance elements.Based on the model,the Bragg scattering and local resonance corresponding to mass defects and local resonances are elucidated,and the effect of the number of defects on the propagation characteristics of flexural waves is revealed by calculating the transmission coefficients of lattice chains with these two defects.Secondly,by adjusting the mass of the mass defect atom and the resonant frequency of the local resonant unit,the bending wave transmission characteristics of the lattice chain are studied.Finally,the effects of axial strain and damping on the transmission characteristics of flexural waves in lattice chains are investigated by applying axial stress and damping on lattice chains.The calculated results show that with the increase of the number of mass defects or local resonance units,the transmission coefficient should decrease gradually due to the periodic arrangement of defects,and finally the bandgap of flexural wave is formed.The width and quantity of the bandgap generated by Bragg scattering in brillouin zone are changed by the atomic mass of mass defect.When the distance between the Bragg scattering bandgap and the local resonant bandgap is close,the interaction results in the lattice chain with a small number of defects can still generate a wider flexural bandgap.The effect of strain on the bandgap of flexural wave in lattice chain is only the shift of bandgap position,but the strong attenuation of flexural wave can be produced by increasing damping,and this attenuation is particularly obvious at high frequency.This research can further improve our understanding of the propagation properties of flexural waves.The propagation characteristics of flexural wave are studied from the perspective of vibration.Firstly,we establish a one-dimensional finite lattice dynamics model with mass defect atoms and local resonance elements.Based on lattice dynamics theory and vibration theory,the amplitude-frequency responses of the flexural waves in these models are calculated respectively.Secondly,the effects of axial strain and damping on the amplitude-frequency response are studied.By comparing the transmission coefficient of infinite lattice chain and the amplitude-frequency response of finite lattice chain,we find that the results obtained from studying the propagation characteristics of flexural waves from the Angle of wave and vibration are highly consistent,which also verifies the accuracy of the calculated results.