Numerical And Experimental Investigation On Band Gap Engineering Of Phononic Crystals

Phononic crystals (PCs) are a kind of acoustic functional materials which have periodic structures and exhibit elastic wave band gaps where the propagation of elastic/acoustic waves is forbidden. This unique feature of PCs provides new prospects for engineering application such as sound insulation, noise control or the design of acoustic devices. Therefore, the topic has received a great deal of attention in recent years. In this thesis, a finite element method (FEM) for band structure calculation of PCs is developed based on the standard finite element software Abaqus by taking advantage of its large-scale calculation, speed, accuracy, etc. Several problems for the engineering of band gaps and defect states by adjusting the geometry structural parameters are investigated:1.An FEM for band structure calculation of solid/solid PCs is developed based on Abaqus. And the speed and accuracy of the plane wave expansion (PWE) method are improved by using the Lapack eigenvalue solver. Numeric results show that the Lapack eigenvalue solver indeed can significantly improve the speed and accuracy of the PWE method. However, the improvement of the convergence and speed of the FEM is more distinguished. The above methods are applied to analyze the band structures of the two-dimensional (2D) solid/solid PCs with simple or complex lattices and the three-dimensional (3D) solid/solid PCs. Compared with 2D PCs with simple lattices, those with complex lattices are easy to open more band gaps in the lower frequency region when the radius of the scatterers is small. The 3D face-centered cubic structures exhibit wider band gaps if the spheroid scatterers' radius or the filling fraction is the same; and the spheroid scatterers can open wider band gap than the cubic scatterers.2.By considering the fluid-solid interaction between the scatterers and the matrix, the Abaqus-based FEM is extended to band structure calculation of the solid/fluid and fluid/solid mixed PCs. The numerical results show that the method is precise and efficient. Especially, it can overcome the disadvantages of the PWE method by removing the unphysical flat bands when the PWE method deals with the fluid/solid systems, and can yield the physical flat bands associated with the resonant modes of the fluid scatterers. These flat bands will disappear with the density of the fluid scatterers increasing. Finally, the developed method is used to calculate the band structures of the 2D and 3D solid/fluid PCs with Helmholtz resonators. The results show that a narrow band gap will appear in the lower frequency region due to the low frequency resonance of the Helmholtz resonator. The width and position of this narrow band gap can be tuned by the structural parameters of the Helmholtz resonator.3.Combined with the supercell technique, the Abaqus-based FEM is extended to band structure calculation of the 2D and 3D PCs with point, line and surface (for the 3D case) defects. The applications of the defect states in the design of the micro resonant-cavity and waveguide. Moreover, the design of the waveguides, splitters and couplers based on solid/fluid phononic crystals is studied numerically by the FEM and experimentally by the ultrasonic measurements. The results show that the wave transmission characteristics of the waveguides, splitters and couplers can be adjusted by introducing resonance units with various structures.4.Based on the 3D wave theory and the thin/thick plate dynamic theory, the Abaqus-based FEM is extended to calculate the band structues of the Lamb waves and bending waves in 2D solid/solid PC plates with simple lattices or Archemedean-like lattices. The results show that the first complete band gap of the Lamb waves is determined by the antisymmetric modes, i.e. the bending wave modes. Therefore, the bandgap characteristics of the PCs plate can be investigated by the plate theory. When the thickness of the plate is small, the solutions based on the thin and thick plate theories have a good agreement. However, with the thickness of the plate increasing, the thin plate theory fails to describe the dynamic bending behavior of the plate. In addition, it is shown that the 2D PC plates with the Archemedean-like lattices are easy to open more band gaps of the bending waves than those with the simple lattices when the radius of the scatterers is smaller, and that the 2D PC plates with the simple lattices are easy to open wider band gaps of the bending waves than those with the Archemedean-like lattices when the radius of the scatterers is larger. With the thickness of the plate increasing, the band gaps show a tendency to increasing and combination.