Evolution of Low-Frequency Band Gaps Using X-Shapes and Single-Sided Stubbed Phononic Crystals
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volution of Low-Frequency Band Gaps Using X-Shapes and Single-Sided Stubbed Phononic Crystals Ahmed Nagatya, Ahmed Mehaneya,*, and Arafa H. Alya a
Physics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt *e-mail: [email protected] Received August 20, 2019; revised August 30, 2019; accepted September 18, 2019
Abstract—In this work, the evolution of dispersion relations of 2D asymmetric phononic crystals in the low-frequency range is introduced and discussed. Two phononic crystal structures are proposed and calculated using Finite Element method. The first one is a thin plate from PDMS with a circular one-side stubbed from tungsten and the other is a thin plate in the X-shape from rubber and tungsten. The effects of some parameters such as stub height and diameter on the phononic band gap value are studied. Low-frequency band gaps can be found in both structures with frequencies corresponding to the audible sound frequency range. The symmetry and shape of the stub has a remarkable influence on the band structures. Where, the proposed one-side stubbed exhibits a phononic band gap in a lower frequency range compared with the published studies about the double side stubbed. Furthermore, with the same thickness value the band gap value was reduced in the X-shape phononic stub compared with the one-side stubbed. These results may be useful for the low-frequency and noise suppression devices. keywords: phononic crystals, stubs, phononic band gap, dispersion relations, x-shape, unit cell DOI: 10.3103/S0025654420020028
1. INTRODUCTION Recent progress in the field of photonic crystals encouraged researchers to devote great efforts in the field of elastic and mechanical waves. Phononic crystals (PnCs) are the mechanical analogue of photonic crystals [1–3]. With the help of PnCs elastic, acoustic and different types of mechanical waves are not allowed to propagate through the so-called phononic band gaps [4–6]. PnCs structures consist of two or more materials with different mechanical properties [7–9]. Due to their novel and variety of physical properties, they can contribute in many engineering applications over large frequency range from noise suppression to thermal management [10–12]. Also, PnCs can introduce innovative application in the field of acoustics imaging, liquids sensing, Resonators, filters and high Q cavities [13–16]. Moreover, more researchers pay more attention on investigating the elastic and acoustic waves propagation defected PnCs structures [17–19]. From the beginning of the field of PnCs and photonic crystals so far, most of the published papers are focused on the Bragg’s scattering mechanism in the formation of phononic band gaps [19, 20]. Such mechanism makes great challenge to the PnCs and limits the applications of such materials especially at the low frequency regime. According to Bragg’s mechanism, it is hardly to obtain low frequency band-gap in PnCs with small dimensions because the wavelength is inversely proportional to the frequency of elastic waves (ω ∝ 1/λ
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