Study On The Tunability Of The Band Gaps And Their Vibration Reduction Performance Of Phononic Crystal Plates

Phononic crystal plates are phononic crystals with a finite size in one direction. Because the existence of Lamb wave band gaps, in which the propagation of Lamb waves is forbidden, phononic crystal plates have attracted great attention of experts and scholars at home and abroad. Lamb wave band gaps have great potential applications in vibration, noise reduction and acoustic device. So how to reduce band gap frequencies, broaden band gap width and enhance tunability of band gaps is the main problem to solve when we investigate phononic crystal plates.Based on the existing basic theory and calculation methods of phononic crystal plates, the band gaps and vibration reduction performance of band gaps in different phononic crystal plates are investigated deeply. We analyze band gap properties by changing the geometrical parameters, material properties, magnetic boundary conditions and so on. The numerical calculation results show that the band gaps can be pushed to lower frequency domain, broadened, and vibration reduction performance of band gaps can be enhanced. The main work is shown as follows:(1) The propagation of Lamb waves in a one-dimensional phononic crystal(PC) slabs bordered with asymmetric uniform layers based on the plane wave expansion(PWE) method and finite-element method(FEM) is theoretically investigated. We investigate the evolution of band gaps and vibration reduction performance of band gaps in the phononic crystal plates with loading layers(layer) arranged from two symmetrical loading layers to single loading layer gradually. Compared with symmetric case, the asymmetric case will generate a new band gap in the lower frequency range. This new band gap results from the opening of the crossing point of different Lamb wave modes. The vibration reduction performance is also investigated by analyzing the transmission power spectra. Finally, the effects of thickness difference, total thickness or the material property of the loading layers on the variation of the band gap width and frequency are studied. The numerical results show that the band gas in this kind of system can be tuned obviously by changing the thickness of the substrate or the superst rate or material property of loading layers. Especially the two edges of the first band gap change approximately linearly with the increase of thickness difference of the two loading layers when the material of the substrate is the same as that of the superstrate.(2) A homogenous plate with periodic tapered surface is proposed. Lamb wave band gaps and their vibration reduction performance in this structure is studied by using FEM and eigen-mode matching theory(EMMT). Compared with the case bordered with asymmetric loading layers, this structure can generate lower band gaps due to the interaction between Lamb wave modes in the plate and local ly resonant modes in the tapered surface. The modes on the lower and upper edges of the lowest three band gaps are studied to identify the physical mechanism of the three lowest band gaps. The vibration reduction performance is also investigated by analyzing the transmission power spectra. Compared with the stubbed case, the tapered case has better performance in vibration reduction.The effects of the geometrical parameters(including the ratio of the lower base width to the upper base width, and the ratio of the upper base width, the thickness of the tapered surface, and the thickness of the homogenous plate, respectively, to the lower base width) on the band gaps are investigated. Numerical results show that the band gaps can be effectively shifted by changing the geometrical parameters.(3) The propagation properties in a homogeneous plate with periodic truncated cones for the square lattice based on the FEM are investigated. The modes on the lower and upper edges of the band gap are studied to identify the physical mechanism of the band gap. As comparison, the band structure of the system with the upper base wider than the lower base is also studied. The result shows that the complete band gap disappears, but there exists a direction band gap, which is also useful in vibration reduction. Finally, we investigate systemically the change of semiangle on the band gap width and position. The band gap can exist in a large range of semiangle and the width of the band gap first increases to a maximum width and then reduces a minimum width when the semiangle increases. But the position of the band gap is pushed to higher frequency domain with the increase of the semiangle.(4) Magnetoelastic materials are introduced into one dimensional phononic crystal plate. The band structures of Lamb mode waves in these structures by using the FEM and the PWE method are presented. Magnetoelastic materials are used as a kind of controllable material to tune the band gap. Numerical results demonstrate that magnetic boundary condition has significant effect on the width and edge s of the first band gap. Compared with the NM case, the two edges of the band gap for the OC and SC cases are pushed to higher frequency region due to the increase of the effective elastic constants. Finally, we investigate filling fraction, plate thickness to lattice pitch ratio and constituent materials on the band gap.In summary, the dissertation systematically investigates the propagation of Lamb waves in different phononic crystal plates. T he band gap formation and tuning mechanisms are clarified, and some important research results have been achieved. The principal countributions are summarized as below: 1) A one-dimensional phononic crystal(PC) slabs bordered with asymmetric uniform layers is proposed, which can generate a lower band gap and the two edges of the band gap have linear relation with the thickness diffrence of loadin g layers. 2) One and two dimensional phononic crystal plates with periodic tapered surface are proposed, which can lower band gaps and enhance the vibration reduction performance. 3) Magnetoelastic materials are introduced into one dimensional phononic crystal plate to tune the band gap. The research results in this dissertation offers an important theoretical basis to reduce structural vibration and design acoustic advices.