Analysis Of Band GAP Characteristics Of Periodic Frame Structure Composed By Composite Beam

Due to the advantages of simple structure,low cost,being easy to be manufactured and assembled,etc.,the periodic structure has been widely used in engineering,marine machinery and aerospace.The typical structures include space deployable structures such as space stations and solar panels.Previous studies of elastic wave propagation in periodic structures show that: specially designed artificial periodic structures have band gaps,on which the waves in certain frequency ranges cannot be propagated;and the position,width,and inhibitory ability of band gaps can be adjusted by changing the material parameters,shape and size of periodic structure.In addition to material parameters,the existing adjustment methods include composition of the structure,structural size,number of units,attaching local resonance(LR)units and regulating the structural defect modes.Wherein,the frame structure with locally resonant units has a relatively low frequency LR band gap,and which can be coupled with the Bragg band gap of the structure.The frame structure with local defect gives some gap splitting phenomenon or multiple transmission spikes in the original band gap position,which has a certain reference value to the band gap design.In this paper,in order to satisfy the stop-band requirements in some special fields,the traditional beam with regular cross-section is expanded to a composite beam or a composite beam with LR unit,the band gap characteristics of the frame structure containing these composite members are studied,and the effect of local defect on band gap characteristics of frame structure are discussed,too.The main work and innovative results are as follows:For the one-dimensional(1D)composite beam periodic structure,a mathematical model of elastic wave(longitudinal wave,torsional wave and flexural wave)propagation in this structure is established,and a kind of calculation method of Bragg band gap and boundary frequency is proposed.Firstly,the wave equations of elastic wave including the transmission matrix and state transition matrix are derived based on the theory of traveling wave.The equivalent characteristic equations of the wave number are established combining Bloch theorem.The law of elastic wave propagation in 1D composite beam periodic structure is analyzed.Secondly,the Bragg frequency calculation formulas of elastic wave are derived by using the theories of solid physics and wave propagation.The computational models of the center frequency and boundary frequency of the band gap of the 1D composite beam periodic structure are established based on the obtained equations of elastic wave equivalent characteristics.And then the band gap characteristics of 1D composite beam periodic structure are analyzed.The results of the study and related Ansys simulations show that the calculation method is certainly correct and accurate.For the two-dimensional(2D)periodic frame structure,a virtual full component model based on the characteristics of the frame structure itself is established and an improved rigidity assembly method is proposed,the band gap characteristics of the 2D frame structure composed by composite beam are studied.Firstly,the spectral element equations of longitudinal wave and flexural wave are derived by using spectral element method(SEM).The whole stiffness matrix and spectral element equations of the 2D periodic frame structure are derived combining with the framework topology information and the proposed improved assembly method.Secondly,based on the 2D periodic frame structure spectral element equation,the influence law of design parameters on the band gap characteristics of the frame structure band is analyzed,such as unit number,structure length,subunit length ratio and frame structure angle,etc.The results show that SEM is suitable for the analysis of highfrequency dynamic response and the band gap characteristics in periodic frame structure.For the 2D periodic frame structure with locally resonant units and local defects,the influence law of spring-mass oscillator on LR band gap and that of locally defect state on Bragg band gap are studied.Firstly,spring-mass oscillator is attached to the joint surface of the composite member to form the composite member of LR type.Then the 2D periodic frame structure is constructed based on these composite beam structural members,and the influence law of the spring-mass oscillator on Bragg and LR band gap is studied.Secondly,locally member defects are introduced into the periodic frame structure without LR units.The influence of different defect combinations on the Bragg band gap on 2D periodic frame structure is studied.The results show that the periodic frame structure with local defects has a tendency to split the band gap.For the cable-beam combination structures,the band gap characteristics of three-dimensional(3D)periodic cable-beam frame structure with cable is studied.Firstly,the motion governing equations and spectral dynamics equations of cable elements are derived.Combining the characteristics of tension-compression,bending and torsion and the improved stiffness assembly method,the general stiffness matrix and spectral element equations of cable-beam combination structures are derived.Secondly,taking the ADAM extension arm as an example,the band gap characteristics of 3D periodic frame structure with cable is studied.The influence of design parameters including the material properties,structure size and number of elements on the band gap of the structure is studied,and the influence of local defects with different modes on the band gap of the structure is studied,too.The results show that the finite number of periodic elements can be approximated when solving the band gap problem of 3D periodic frame structure with cables.The results also show that the original band gap has a tendency to split when the 3D periodic frame structure with cables has periodic defects of structural member.