Modulation Of Band Gap Characteristics In Phononic Crystal Structures Of Magneto-elastic Particle Chains

Phononic crystal is a class of engineered media composed of periodic arrays of scattering inclusions in a homogeneous host material.Phononic crystal can be directly applied to mechanical frequency filtering and sound insulation because of the existence of band gap.In recent years,in order to realize the active regulation of phononic crystal band gap,many solutions have been proposed by researchers;These include geometric changes to the structure by applying external stresses and changes to the elastic characteristics of the constitutive materials through application of external stimuli,like an electric field,temperature changes,or a magnetic field.Among the various proposed phononic crystals,granular crystals,which are closely packed ordered arrangements of elastic particles(mainly spheres)in contact,due to the Hertz contact interaction between the particles,the dynamic vibration response of these structures may be nonlinear.These nonlinearities can present abundant physical phenomena.In order to realize the active regulation of the band gap and study the effect of nonlinearity on the band gap,the band gap characteristics of particles of iron and aluminum is studied.Also,the regulation of the magnetic field and particle mass distribution on the band gap characteristics is investigated in this reasearch.In addition,the phononic crystal transmission spectrum of particles chain phononic crystals of iron and aluminum is tested by a Laser Doppler vibrometer.At the same time,the influence of the nonlinearity of the particle phononic crystal structure on the band gap is calculated by using the perturbation method and the harmonic balance approach respectively.Specific research contents are as follows:(1)Firstly,the band gap adjustment of phononic crystals with alternating ferromagnetic spheres and aluminum spheres under different magnetic field intensities is studied,and the band structure of particle chains with different mass distributions is analyzed by changing the radius of one of the particles.In this study,the band gap distribution and range of particle chains with different mass distribution under different magnetic field intensities were obtained by numerical calculation method.By adjusting the intensity of the magnetic field and changing the radius of one of the particles,different band gap ranges are obtained so as to achieve the purpose of non-contact active band gap regulation.Then,based on the phononic crystal test platform built by the research group,the transmission spectrum of the magnetic particle chain phononic crystal is tested,and the comparison with the numerical results shows that the two are in good agreement,thus verifying the reliability of the numerical results of particle chain phononic crystal system band gap calculation.(2)Based on the research of Elastic Wave Propagation in Weakly Nonlinear Periodic Structure and considering the nonlinear particle contact,to study the ferromagnetic and aluminum particle chain with piezoelectric spring arranged alternately nonlinear phononic crystal in different magnetic field intensity,the positive and negative proportional control of piezoelectric spring,hard and soft nonlinear effect on the band gap,and by changing the method of particle radius analysis magnetoelectricity elastic particles chain the influence of different mass distribution on the band gaps.This research can be applied to new elastic wave devices with active control and nonlinear characteristics.Based on the Lindste-Poincare method,the approximate solution of the dispersion relation is derived,and the possibility of active control of elastic waves in weakly nonlinear lattice chain phononic crystals is discussed.In order to reflect the characteristics of nonlinear elastic wave mechanics,the band gap adjustment of elastic wave amplitude,degree of nonlinearity,hard nonlinearity and soft nonlinearity is mainly studied.By changing the magnetic field and electric field,we can control the band gap actively and study the nonlinear effect on the band gap.(3)On this basis,the dispersion relationship in one-dimensional magnetic particles chain phononic crystals with iron aluminum is studied by the generalized harmonic balance method.The proposed method is used to predict dispersion relations in strongly nonlinear chains with Hertz contact interactions.Both the cutoff frequency and band gap of magnetic particles of iron and elastic particles of aluminum particle chain phononic crystals depend on the amplitude.The trend of amplitude dependent dispersion predicted by harmonic balance method is consistent with that predicted by perturbation analysis.In fact,this study describes the variation of the effect of low and high amplitudes on the band gap in a nonlinear magnetic particles of iron and elastic particles of aluminum particle chain phononic crystals.