Study Of The Influence Of Geometric And Material Parameters On The Vibration Band GAP Of Periodical Beam Structure

Since long ago,the control of structure vibration has always been paid attention to theoretically as well as in the engineering domain,which is also an important issue to be solved.Periodic beam structure is commonly seen in engineering.Meanwhile,it has a very significant property which is called the band gap.When the elastic wave propagates in periodic beams,it exists a certain range of frequency within which the wave can't propagate.This frequency range is the band gap.It is a promising method to take advantage of this property of periodic structure to control vibration in practical application.Because compared with those traditional ways of vibration attenuation,it's possible to realize our aim simply by using the structure itself.By combining theoretical analysis with finite element method,the vibration bandgap characteristics of periodic beam structure are studied in this paper.The main research contents are as follows:Firstly,the wave equation of periodic beam structure is summarized in the theoretical part,and Bloch's theorem is used to describe periodic beam structure.In addition,combined with Bragg reflection,the longitudinal vibration band gap of beam is explained.Then,the calculation methods of band gap are introduced,and combined with the beam structure studied in this paper,the finite element method is selected.The settings of the model and the parameters and the procedure of calculation by finite element method are explained in detail.Then by performing a large amount of calculation by the finite element software Comsol Multiphysics,the effects of material parameters including Young's Module and the density on the band gap characteristics considering the coupling of longitudinal and flexural vibration of periodic beam of equal cross-section are studied.Then the influence of geometric parameters and the material composition on the frequency range and the width of band gap are also studied.Secondly,the influence of geometric parameters on the bandgap of trapezoidal periodic beam with variable section is studied.The influence of size change on the bandgap of periodic beam structure formed by a single material,and the influence of size change on the bandgap of periodic beam formed by two materials are respectively considered.Finally,the influence of the material composition on the band gap properties of periodic beam composed with three materials is studied.Based on the study of the influence of the parameters above on the position and width of the band gap,conclusions are reached,which provide a reference for the design of periodic beam structure with specific band gap for the practical application of vibration attenuation.