| Phononic crystals are defined as a type of composite periodic structure that can block the propagation of acoustic or elastic waves in a certain frequency range.The forbidden band properties of phononic crystals allow for a wide range of applications in areas such as vibration and noise reduction,filters,and acoustic sensors.One of the most important issues for Pn Cs is band gap active adjustment.In recent years,it is a significant way to adjust the band gap of phononic crystals by introducing smart materials to prepare phononic crystals and using external stimuli to adjust their band gap structure.Hard-magnetic soft material is a new type of magnetically sensitive smart material that has emerged in recent years,made by 3D printing technology by homogeneously embedding some hard-magnetic particles(e.g.Nd Fe B particles)into a silicone rubber matrix.Under the excitation of external magnetic field,the hardmagnetic soft material is subjected to magnetic torque to achieve fast,complex and programmable 3D shape changes.In this paper,by introducing the hard-magnetic soft material into phononic crystals,the regulation characteristics of the external magnetic field on the elastic wave band gap of the hard-magnetic soft material phononic crystals are studied by the finite element method,and the remote driving of the external magnetic field on the shape of phononic crystals and the active regulation of the elastic wave band gap are realized.The specific research of this paper includes:(1)The theoretical basis and controlling equations of elastic wave propagation in hard-magnetic soft material phononic crystals are introduced based on the neoHookean hyperelastic model.A hard-magnetic soft material sample was prepared using 3D printing equipment,and the shear stress-strain curve of the hard-magnetic soft material sample was measured by a universal material testing machine with a self-made dual-lap shear test fixture,and the shear modulus of the sample was calculated based on the curve.Next,the magnetic hysteresis loop of the hardmagnetic soft material samples were measured using a vibrating-sample magnetometer to obtain the magnetization of the samples.These basic works were carried out to lay the foundation for the calculation of magnetically controlled deformation and band structure of the hard-magnetic soft material phononic crystals.(2)The elastic wave band gap properties of two-dimensional periodic porous hard-magnetic soft material phononic crystals under the applied magnetic field are investigated.A finite element model of hard-magnetic soft material phononic crystals with different magnetic anisotropy encoding is developed,and the effects of magnetic field,structure thickness,structure porosity and different magnetic anisotropy encoding modes on the band gap structure are discussed.The numerical results show that it is very effective to adjust the start frequency,stop frequency and band gap width of the hard-magnetic soft material phononic crystals by applying the external magnetic field,and the external magnetic field can regulate the generation and closure of the band gap of the hard-magnetic soft material phononic crystals.Different magnetic anisotropy encoding modes have significant effects on the number of band gaps and the critical magnetic field of the band gaps,and the number of band gaps and the critical magnetic field of the band gaps significantly depend on the complexity of the magnetic anisotropy encoding modes,encoding mode III has a larger number of band gaps and a larger critical magnetic field for the band gaps.In addition,it is found that the thickness and porosity of the structure also have a significant effect on the band gap regulation of two-dimensional periodic porous hard-magnetic soft material phononic crystals.(3)In order to realize the active adjustment of the broadband and multiband characteristics of phononic crystals,hard-magnetic soft materials are introduced into lattice phononic crystals,and encodable soft lattice phononic crystals structures with sinusoidal ligament shapes are established,and the effects of magnetic fields,the number of ligament peaks and applied mechanical loads on the band gap structures are analyzed.The results show that the sinusoidal ligament encodable soft lattice phononic crystals have more obvious broadband and multiband compared with the two-dimensional periodic porous hard magnetic soft material phononic crystals,and the soft lattice phononic crystals are superior to the two-dimensional periodic porous structures in terms of maximum band gap width and number of band gaps.The external magnetic field can deform the straight ligament into a sinusoidal ligament and open the new band gap effectively;and the number of wave peaks on the ligament has a significant modulating effect on the position of the elastic wave band gap and the band gap width leading to broadband and multiband characteristics.Changing the magnetic encoding mode of the structure allows active adjustment of the low and high frequency broadband,respectively,with encoding modes III and IV effectively adjusting the low frequency broadband and encoding modes V and VI effectively adjusting the high frequency broadband.In this chapter,the authors also discuss structural magnetic anisotropy encoding modes that can effectively induce lowfrequency broadband and high-frequency multiband;the combined magneticmechanical forces on the bandgap of the elastic waves of sinusoidally ligamentous encodable soft lattice phononic crystals are investigated,where mechanical loading can cause the structure to branch into new deformation modes,and the tunable frequency range of the bandgap is significantly increased,demonstrating a wide range of bandgap tunability.(4)A three-dimensional phononic crystal model of hard-magnetic soft material is established,and the elastic wave band gap regulation of the three-dimensional phononic crystal of hard-magnetic soft material is carried out.The results show that under the excitation of external magnetic field,the three-dimensional phononic crystal of hard-magnetic soft material can realize the simultaneous regulation of lowfrequency band gap and high-frequency band gap,and the band gap frequency can occupy the whole dispersion region as much as possible,and the band gap regulation ability is more prominent than that of the two-dimensional phononic crystal of hardmagnetic soft material.The unidirectional magnetic field can lower the band gap frequency and shift the band gap downward,while the application of bidirectional magnetic field can effectively open the low-frequency band gap of hard-magnetic soft material three-dimensional phononic crystal.In addition,the band gap width of the low-frequency bandgap of the three-dimensional phononic crystal is significantly increased by changing the magnetic encoding modes. |
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