Research On The Band Gap Of Pre-deformed Phononic Crystals

The elastic wave propagation in periodic composite materials or structures has been studied in depth and researchers have discovered that these materials or structures can prohibit the propagation of certain elastic wave frequencies.These frequency ranges are called band gaps and the materials or structures with elastic band gaps are called phononic crystals.At present,the calculation methods of elastic wave band gap characteristics mainly include the transfer matrix,the plane wave expansion,the finite difference time domain,the multiple scattering theory,the lump-mass and the finite element.The finite element method is used to study the influence of different loading conditions on the band gap of two-dimensional and three-dimensional phononic crystals with the hyperelastic and same tension-compression modulus in this paper.A single cell was established in ABAQUS.Periodic boundary conditions were applied to the two-dimensional and three-dimensional phononic crystal unit cells by python script,and initial buckles were introduced.After loading,the band gaps of 2D and 3D phononic crystal structures under pre-deformation were studied.Representative units are used in the research process,whether it is a two-dimensional or three-dimensional phononic crystal structure.For two-dimensional phononic crystals with the same tension-compression modulus,the band gaps under five loading states are studied: uniaxial tension,uniaxial compression,biaxial tension,biaxial compression,and simple shear with biaxial compression.The studies of three-dimensional phonon crystals add two loading conditions,triaxial tension and triaxial compression.For two-dimensional phononic crystals with tension-compression asymmetry materials,the initial band gap was studied by fixing the relevant modulus of compression,changing the relevant modulus of tension,and adjusting the ratio of tension’ and compression’ modulus.Studies have shown that different loading conditions have a great impact on the generation of new band gaps,the stability of the main band gap,the disappearance of the main band gap,and the position of the band gap during the loading process,and the main band gap and the new band gap can be realized by adjusting the axial loading ratio.For two-dimensional phononic crystals with tension-compression asymmetry materials,studies have shown that the position of the initial band gap is affected by the tension-compression modulus,but it does not change the normalized width of the band gap too much.These systematic studies provide potential applications for some sound filters,acoustic wave guides,vibration isolators and phonon devices.