The Propagation Characteristics Of Elastic Waves In Phononic Crystals

Phononic crystals are periodic elastic composite materials with band gaps where the propagation of elastic waves (ELW) is forbidden. This property provides new prospects for technology of noise and vibration attenuation, which have been one of the pop research topics in academic and engineering for a long time.As the counterparts of photonic crystals in elasticity, phononic crystals open new avenues to control the sound and vibration precisely, for the propagation of ELW in artificial periodic structure can be analyzed accurately using band theory. For the engineering application, the formation mechanisms of the band gap, as well as the mechanical and acoustical properties of the phononic crystals, are crucial problems. Therefore it is of fundamental importance to gain a clear understanding of the above problems by the study on the ELW propagation behavior in phononic crystals. In this dissertation, based on the multiple-scattering model of phononic crystals, the formation mechanisms of the band gap, as well as the physical mechanism of the mechanical and acoustic properties of phononic crystals are investigated deeply and systematically. The main work and achievements are as follows:1. The propagation behavior of elastic waves in phononic crystals are evaluated and explained explicitly by the study that both the periodic structural factor and the unite cell's factor are involved simultaneously. These two factors are extracted in the analysis of band structure, the influence of them are discussed separately and combined. It has been concluded that the propagation behavior of ELW in phononic crystals can be studied deeply by this method.2. The uncoupling effects stem from the symmetry of the structural periodicity has been found in the phononic crystals as the band gaps open. Then an analytic formula that comprises the periodic structural factor and the Mie scattering of a single inclusion simultaneously has been achieved to describe the modes at the edge of the first gap. On this basis, the contribution of these two factors to the formation of the first band gap is analyzed quantitatively. It gives a clear understanding for the formation mechanism of the full band gap and the vary rules of the first band gap. As well as the inner relationship and difference between the Bragg mechanism and the local resonance mechanisms are studied deeply.3. Elastic wave scattering and dynamic stress concentration in two-dimensional phononic crystals are analyzed systematically. A marked increase of dynamic stress concentration due to the periodic structural factor is found at the edge of the band gap. It has been found the first-order uncoupling mode is the key factor of the formation of the dynamic stress concentration.4. According to the behavior of the Mie scattering of a single inclusion and the periodic structural factor in the long-wavelength limit, exact analytical formulas for the effective velocities of elastic waves in phononic crystals are derived both for solid and fluid (or gas) matrix. The influence mechanism and rule of the effective velocities are studied in detail, and the key factor that influences the anisotropy of the effective velocities in the phononic crystals is found and proved.In summary, drawn by the application of vibration and noise control, the formation mechanisms of the band gap as well as the physical mechanism of the dynamic stress concentration and the effective velocity of phononic crystals, are investigated deeply by developing a systemically investigation that evaluate the influence mechanism of the periodic structural factor and the single unite cell's factor separately and combined. The research results in this dissertation are meaningful in both the theory of the PCs and its engineering application in vibration/noise control.