Energy Harvesting Based On Defect Modes In Phononic Crystal Beams

Phononic crystals(PCs)are a kind of periodic structures.They have elastic or acoustic waves band gaps.The characteristics of band gaps show that elastic or acoustic wave propagation is strongly forbidden inside the band gaps.When the periodicity of a PC is disturbed or slightly destroyed,defect bands might arise inside the original band gaps.The elastic waves or acoustic waves corresponding to the defect modes are localized at point defects or propagate along linear defects.At present,research of non-perfect PCs is mainly focusing on theoretical calculations and relating experiments are relatively few.In this thesis,the band structure of a PC beam is studied theoretically and its transmission characteristics are experimentally validated.We also apply the defect modes to efficiently harvest the flexural wave energy.The main research work is as follows:(1)A transfer matrix method(TMM)based on Timoshenko beam theory is built,which is more accurate than that based on the Euler-Bernoulli beam theory,to obtain the band structures of a PC beam.Using a supercell technique comprising a point defect,we acquired band structures with defect modes and found that the defect modes inside the band gaps are bands shifted from some of the bands of the original dispersion curve.The influences of the length of unit cell,the height of the defect,and the Young's modulus of the defect are investigated in this thesis.In addition,the location of the band gaps and defect modes of the PC beam are found to be particularly sensitive to the lattice length.(2)To the best knowledge of the author,this is the first time the point-wise fiber Bragg grating(FBG)displacement sensing system is employed to obtain the displacement transmission FRF and to experimentally study the slow flexural waves around the defect modes of the PC beam.Transient wave packet propagation is experimentally measured at 35 different frequencies ranging from 300 Hz to 900 Hz using 21-count Hanning windowed tone burst excitation signals.Slow propagation of flexural waves via defect coupling in the phononic crystal beam is then clearly demonstrated by calculating the group velocities of the bending waves.Good agreements between FBG transient measurement and finite element method(FEM)simulations can be obtained.Through the transient displacement fields of the PC beam around the defect modes,we see that the localized defect modes cause wave propagation in a standing wave mode in the PC beam.(3)Taking dual advantages of the localization of flexural waves due to a point defect placement of a piezoelectric power generator near the excitation source,we designed a PC beam with a point defect for efficient flexural waves energy harvesting.The polyvinylidene fluoride(PVDF)film is placed around the point defect of the PC beam for energy harvesting.The maximum harvesting output power based on the first defect mode(615Hz)and second defect mode(2688Hz)are 54.4nW and 777.5nW,respectively.Both values are higher than those harvested from excitations at resonant frequencies of the PC beam.A theory for energy harvesting of the PVDF film generator is also developed to predict the output voltage and power in the PC beam.Good agreements can be obtained between the experimental measurements and the theoretical predictions.