Abstract
Using the finite element method, we have studied the acoustic properties of a novel phononic crystal (PC) structure constructed by periodically depositing single-layer or two-layer stubs on the surface of a thin homogeneous plate. Numerical results show that the extremely low frequency band gap (BG) of the Lamb waves can be opened by the local resonance (LR) mechanism. We found that the width of such a BG depends strongly on the height and the area of cross section of the stubs. The displacement field distribution of the oscillating modes is given to explain how the coupling of the modes induces the opening of the BG. The physics behind the opening of the LRBG in our phononic structures can be understood by using a simple 'spring-mass' model.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. In the past decade, many works have studied the propagation of elastic waves in composite periodic materials, the so-called phononic crystals (PC). Because of their ability to create acoustic band gaps (ABGs), the PCs have many potential applications, such as confinement, filtering and wave guiding. The principal mechanisms responsible for the creation of ABGs are Bragg scattering and local resonance (LR). For the first mechanism, the band gap usually falls into the wavelength in the order of the structure period; but for the second, a resonant ABG is imposed by the frequency of resonance associated with scattering units. Generally, the ABG frequency range based on LR can be almost two orders of magnitude lower than the usual Bragg gaps.
Main results. Our paper shows how we can open extreme low-frequency ABGs using the LR mechanism. We investigate the case of two simple PC stubbed plates. With these structures, one can easily understand the physics behind the creation of this kind of ABG by employing a 'spring-mass' model and studying the polarisation features of the scattering units. We also show that we can control the width and the localisation of ABGs almost entirely by simply changing a few physical parameters.
Wider implications. The PC structure we studied comprises a great tool for wide applications dealing with acoustic wave propagation in low-frequency regimes, for instance shielding low-frequency noise or building insulation.