Characteristic Study Of Band Gaps In Phononic Crystal Type Periodic Composite Structures

When elastic and acoustic waves propagate in the periodic composite media, maybe some photonic crystals-like band gaps will come into being. That is to say, the propagation of vibration and sound will be forbidden when the frequencies are the range of band gaps. So the concept of phononic crystals (PCs) was brought about. The propagation of elastic and acoustic waves in PCs has received much attention in the world, and a great deal of work has been devoted to the study of band gaps of PCs. The motivation for these studies is to further understand the forming mechanism of band gaps and make great efforts to provide some new idea and approach in vibration and noise control.Based on the research status and basic theory of PCs, the characteristics and effect factor of band gaps in one- two- and three-dimensional PCs are studied. At the same time, the feasibility of building some periodic composite structures with band gaps of PCs for vibration and noise control in engineering structures is presented by making use of the forming mechanism of band gaps of PCs. The main work is shown as following:(1) Using the wave propagation method (WPM), the band gaps of longitudinal wave in one-dimensional PCs are studied. Results obtained using WPM are evaluated against those by plane wave expansion (PWE). It shows that the computing speed of WPM is quicker than that of PWE. Considering the changing of elastic constants with frequency of viscoelastic material, the band gaps can be obtained directly, and the computing time of WPM is far too smaller than that of PWE improved using iterative method.(2) Using PWE, the flexural vibration band gaps in thin plate PCs with two-dimensional binary and ternary units are studied. It is found that the band gaps in low frequency with local resonant mechanism exist in the thin plate PCs with ternary units. The numerical results are used to show how the width of the first full band gap depends on radius ratio, filling fraction and so on. The vibration transmission characteristics of the finite periodic thin plates are simulated by finite element method, which shows that the flexural vibration in finite periodic thin plates will be inhibited seriously in some frequencies which are different from the frequencies of band gaps. And the effect of boundary condition on vibration transmission characteristics in thin plates is also discussed.(3) The characteristics of band gaps in three-dimensional PCs consisting of cubic steel embedded in an epoxy host periodically in simple cubic lattice are studied by using of PWE. Some numerical results are used to show how characteristics of band gaps depend on filling fraction, parameters of scatters and so on. It shows that the pseudo band gaps in some directions can be gotten by modulating the side length ratio of scatters.(4) Using WPM, the flexural vibration band gaps in periodic beams with inconstant section are studied. It is found that the frequencies of band gaps will have some decreases when shearing deform and rotation inertia are considered. And the effects of geometric and physical parameters of beams on band gaps are discussed. Enlightened by the forming mechanism of band gaps of PCs, the impediment to propagation of flexural waves in infinite beams using dynamic vibration absorbers (DVAs) arranged periodically is investigated. And the effects on band gaps of the parameters of DVAs and beams are studied. Then the flexural vibraton transmission characteristic of a finite beam is proposed by finite element method. The numerical results show that the propagation of flexural waves will be weakened greatly in corresponding band gaps of the infinite beams.(5) Using WPM, a method for the calculation of band gaps is deduced for the normal incident noise in one-dimensional PCs of layered plates. Then attention is turned to the feasibility of shielding the noise being sensitive to people in the case of building PCs-like composite plate structures. And the sound insulation of composite plate structures consisting of multilayer Pb-soft rubber and steel-butadience acrylnitrile rubber is presented. The results show that such composite plate structures can lower the starting frequency and widen the band gap by the reasonable modulation and collocation of parameters of PCs.(6) Based on Flügge's shell theory, the band gaps in pipelines composed of a set of periodically repeated elements of two types are investigated by using WPM. It is shown that the band gaps do exist in such periodic pipelines for any circumferential modes. The effects on band gaps of density ratio, stiffness ratio, lattice constant, and thickness of pipelines and so on are discussed. The numerical results show that it is feasible to design a periodic composite structure for deadening the vibration of pipelines.The research results in the dissertation are helpful to apply the concept and principle of PCs to vibration and noise control. The band gaps of some certain PCs-like periodic composite structures presented in the dissertation will provide some new idea and approach in vibration and noise control.