Research On The Tunability Of Band Gaps And Vibration Energy Harvesting Based On Point Defect In Two Dimension Magneto-elastic Phononic Crystals

Phononic crystal as a typical composite material is formed by the different periodic structures,which the band gap properties make it have the wide applications in the vibration isolation,acoustic stealth,acoustic detection and aerospace fields.Meanwhile,the magnetostrictive materials as a typical smart material are sensitive to the external excitation(magnetic field,pre-stress,temperature,etc.)and respond to the external excitation quickly,so it is necessary to investigate the active control of elastic wave in magnetostrictive phononic crystal.On the other hand,owing to the wave localization and enhancement phenomena on account of point defect modes inside the band gaps,vibration energy can be easily converted into electric energy by placing a ceramic piezoelectric patch within the defect state.In order to expand the frequency of band gap and improve the efficiency of vibration energy harvesting,we consider the point defect characteristics,the magneto-electro-elastic coupling interaction of magnetostrictive material and piezoelectric material.Hence,this paper is to present two 2D magneto-elastic phononic crystals structures to modulate the band structures and the range of vibration energy harvesting using finite element method via an applied magnetic field and pre-stress.Specific studies are as follows:(1)A vibration energy harvester is proposed by inserting piezoelectric material into 2D infinite magneto-elastic phononic crystals with point defect from a 5×5 supercell.The 3D nonlinear magneto-elastic coupling constitutive relationship in combination with the supercell technique is adopted to calculate band structure by applied magnetic field and pre-stress along the z direction.Based on the piezoelectric material with linear constitutive equation,the direct piezoelectric effect is used to predict output voltage and power for energy harvesting by the effects of external magnetic field and pre-stress.The numerical results illuminate that the band gaps and defect bands of the in-plane mixed wave modes(XY modes)can be adjusted to a great extent by applied magnetic field and pre-stress.Due to the change of defect band frequency,the displacement field distributions of the defect band frequencies are changed,which leads to variation of the collected energy in the effect of magnetic field and pre-stress,and thus a much large range of vibration frequency and more broad-distributed energy can be obtained.The band gaps and defect bands in the anti-plane wave modes(Z mode),however,have a slight change with applied magnetic field,which leads to a certain frequency range of vibration energy harvesting.In addition,the harvesting of vibrational energy and electrical-mechanical conversion efficiency using point defect modes are highly dependent on the positions of the piezoelectric patch.(2)In order to realize the intelligent control of both band gaps and acoustic energy harvesting,a 2D plate-pillar type magneto-elastic phononic crystal with point defect structure is proposed by periodic array of Terfenol-D pillars deposited on a silicon plate.By applied the vertical magnetic field to the magnetostrictive pillar,the propagation characteristics of Lamb waves in magneto-elastic phononic crystal and the properties of acoustic energy harvesting under different magnetic fields are investigated.The numerical results by the finite element method indicate that the generation and closure of the band gaps are strongly dependent on the applied magnetic field.Moreover,the frequency of defect band and the range of acoustic energy harvesting can be modulated significantly by an applied magnetic field,which leads to broadband band gaps and promotes the electromechanical energy conversion efficiency.Furthermore,the damping of the piezoelectric patch affects the optical load resistance and acoustic energy harvesting.(3)The effect of phononic crystal size(5×5 and 7×7 supercell)on the band gap and defect band was studied for the 2D plate-pillar type magneto-elastic phononic crystal structure with point defect.The numerical results by the finite element method show that not only different supercell sizes affect the band gap width of the phononic crystal,but also have a significant effect on the defect band frequency.At the same time,it is found that the size of the supercell has a remarkable effect on the displacement field distribution at the defect frequency,and then affects the vibration energy harvesting efficiency.