Adjustment And Analysis Of Bandgap Characteristics Of Plate-like And Beam-like Phononic Crystal

The slab and beam structure has been widely used in vehicle,ship,construction,aerospace and other fields.Because of the large flexibility,the slab and beam structure is easy to produce vibration and radiate noises under the external excitation.Therefore,the concept of plate-like and beam-like phononic crystals is introduced to solve the problem of vibration and reduce noises.Unique bandgap characteristics of phononic crystal can suppress the propagation of elastic waves in the bandgap.The phononic crystal structure can adjust the position of the band-gap by changing its material coefficients,geometric parameters,unit cell structure and other factors.Great achievements have been obtianed in the field of phononic crystals.However,these studies foucus on ideal phononic crystals,and ignoring the processing cost,processing error,structural interchangeability and other issues in practical engineering applications.Therefore,we try to make further study of the characteristics of the band-gap and adjustment rules of different plate-like and beam-like phononic crystals,as well as the research principle of actual engineering needs.The main research work and innovations of this paper are described as follows.(1)In order to solve the design problem of specific band-gap design of beam-like phononic crystals,the mechanical models of longitudinal,torsional and bending motions of beam elements are firstly established.The transfer matrix equation of the band-gap of beam-like phononic crystasls is established by combining the continuity conditions of forces and displacements at the nodes with Bloch's theory.Dispersion equations of spatial beam-like phononic crystals are derived forward.The optimal design method of the bandgap of beam-like phononic crystals is proposed.The relative bandwidth(defined by the ratio of the total width of to the lower angle frequency of the band-gap),economic benefit and the degree of processing difficulty are taken as the objective function,and the material coefficient and structural size of beam-like phononic crystals are taken as the design variables.Numerical simulation results verify the validity of the proposed optimization design method.(2)In order to realize the passive adjustment of the band-gap of beam-like phononic crystals,the piezoelectric patches with different shunt circuits are periodically pasted on the matrix beam and forming the beam-like phononic crystals.The equivalent elastic modulus of beam element containing piezoelectric circuits is derived by piezoelectric constitutive equations.The dispersion equation of the beam-like phononic crystals with piezoelectric shunt circuits is derived by combining the transfer matrix method with Bloch theoy.The effects of structural parameters on the characteristics of the band-gap of piezoelectric beam-like phononic crystals are respectively analyzed for piezoelectric circuits with resistor,capacitor,LC,LR and LCR shunt circuits.The results show that the initial frequency of the bandgap can be adjusted in a large range,and several additional band-gaps can be generated by changing structural parameters of piezoelectric patches.(3)In order to explore the influence of the shape and position of the scatterer on the band-gap of phononic crystals,a cell structure with star scatterer is designed for plate-like phononic crystals and its characteristics of the band-gap are investigated by the plane wave expansion method.Based on the periodicity of phononic crystals and Bloch theory,the material coefficients of the plate-like phononic crystal and the particle displacement of the elastic wave are expanded into the form of Fourier series,respectively.Then,the Fourier series expansion is substituted into the wave equation of elastic waves.The dispersion relation and the band-gap diagram of the phononic crystals with star scatterers is obtained.In addition,the effects of the filling rate and position of the star scatterer on the band-gap of phononic crystals are also studied.The results show that the width of the band gap depends not only on the filling rate of the scatterer,but also depends on the shape and position of the scatterer.(4)In order to achieve the interchangeability of phononic crystal structures during band-gap adjustment process,a multicomponent phononic crystals plate is proposed.The unit cell models of two dimensional multicomponent phononic crystal with and without coating are established respectively.The first six disperdion curves of multicomponent phononic crystals with and without coatings are calculated by using the finite element method and Bloch theory.The frequency response of a 5×5 cell and the eigenmodes corresponding to the edge frequency of the band-gap are calculated.The mechanism of the band-gap generation is analyzed.Finally,the influence of the material ratio and scatterer configuration on the band-gaps of two two types of multicomponent phononic crystals are studied.The results show that the change of material properties of the uniformly distributed scatterers can not only adjust the band-gap of plate-like phononic crystals,but also meet the interchangeability requirement of phononic crystals.(5)In order to solve the problem of real-time bandgap regulation of phononic crystals,a plate-like phononic crystals with the slider and stub is designed.The band-gap,frequency response and eigenmodes related to the edge frequency of band-gap are calculated by using the finite element method and the mechanism of band-gap formation is analyzed.At the same time,the influence of the symmetry of the stub,the position of the slider and the material of the slider on the band-gap is studied.The results show that the band-gap of the plate-like phononic crystals can be effectively adjusted in real-time effectively by changing the position and material of the slider.