Effects Of Material Parameters On Band Gaps Of Three-Dimensional Solid Phononic Crystals

Phononic crystals (PNCs) are a kind of composite materials which have periodic structures and exhibit elastic wave band gaps where the propagation of acoustic/elastic waves is fully forbidden. Due to their unique properties and potential applications in sound insulation, noise control, shock attenuation, etc. they have become one of the most important areas in mechanics. condensed matter physics and mechanical engineering, etc. In this thesis, the finite difference time domain (FDTD) method for calculating the band structures of three-dimensional (3D) PNCs is developed, and the accuracy and efficiency of the method are verified. Based on the self-developed FDTD method, we carry out the studies in following aspects:1. The material parameters which determine the band gaps in the 3D solid/solid PNCs are obtained directly from the finite difference form of the elastic wave equations. These material parameters include the transverse wave velocity ratio (ct1/ct2). the acoustic impedance ratio(zt1/zt2) and the Poisson's ratios v1 and v2.2. The effects of the material parameters on the band gaps in 3D solid/solid PNCs with the simple-cubic (SC). body-centered (BCC) and face-centered (FCC) lattices are studied. The numerical results show that:the transverse wave velocity ratio and the acoustic impedance ratio play more important roles in determining the band gaps than the Poisson's ratios do:the band gaps appear in the system with large impedance ratio and small mismatch in the wave velocities, or with small wave velocity ratio and small mismatch in the acoustic impedances; the mid-gap frequency decreases as the wave velocity ratio decreases; the wave velocity ratio is the most important parameter which determines the mechanisms (Bragg scattering or local resonance) of the band gaps and the mid-gap frequencies; band gaps are easily opened in the BCC and FCC systems than in the SC system:with the same filling fraction and the material parameters, the band gaps in the BCC-and FCC-latticed systems are generally wider than that corresponding to the SC-latticed system.3. The band structures of the 3D porous PNCs are studied. It is shown that the Poisson's ratio of the solid host is the unique material parameter which has direct effect on the band structures of a 3D porous PNC. The numerical results show that. in the svstems with the SC, BCC or FCC lattices. the band structure is not sensitive to the Poisson's ratio. and no full band gap can be generated.