Structural Design And Dynamic Characteristics Of Parametric Tunable Phononic Crystals

Noise and vibration suppression are urgent problems to be solved in daily life,industrial development and national defense security.The band gap characteristics of phononic crystals provide a new way to control and avoid the harmful vibration in equipment and noise in environment.For phononic crystals,once the material or geometric parameters are determined,the band structure will be determined and not easy to change.At present,the active control of the band structure of phononic crystals mainly uses materials that can couple with other physical fields,but the band gap of the phononic crystals cannot be effectively regulated,and the band structure of the phononic crystals cannot be arbitrarily changed.Based on this situation,a new method for controlling the band structure of phononic crystals is proposed,which changes the equivalent stiffness of the system by applying high frequency excitation to the phononic crystals system,and then actively adjusts the band structure of the phononic crystals.This paper elaborates the feasibility and validity of this method from the following aspects.Starting from 1-D discrete phononic crystal structure,the dynamic model of phononic crystal unit is established by Lagrange equation,and the motion separation method is used to deal with the excitation term introduced by high frequency excitation in the motion equation.The band structure is obtained by solving the dynamic equation theoretically,and the transmission characteristics of finite phononic crystal are calculated,and the influence of parametric excitation on the band structure of phononic crystal is analyzed.The numerical solution of band structure is carried out by MATLAB,which is verified by comparison with the theoretical results.The research process of 2-D discrete phononic crystal is similar to that of 1-D discrete phononic crystal.Because the direction of elastic wave propagation is also involved in 2-D phononic crystal,the effect of parametric excitation on group velocity is analyzed in the study of 2-D phononic crystal.The 2-D phononic crystal structure which can achieve waveguide effect is designed by changing the band structure caused by parametric excitation,and the numerical verification is carried out.The 2-D phononic crystal element model is constructed by finite element software and the band structure is solved.The vibration modes of phononic crystal element at different characteristic frequencies are analyzed.Finally,the effect of parametric excitation on the band structure of phononic crystal beam is studied.The band structure is solved by transfer matrix method,and the influence of parametric frequency on Bragg band gap and local resonance band gap is analyzed.The band structure of phononic crystal beam at different excitation frequencies are solved by finite element method and compared with the theoretical results.The band structure is validated by constructing a finite structure phononic crystal beam and calculating the transmission characteristics.The response of the finite structure phononic crystal beam in Bragg band gap and local resonance band gap is analyzed to explain the reason why the parametric excitation has different effects on the two band gaps.