Abstract
The quest for large and low frequency band gaps is one of the principal objectives pursued in a number of engineering applications, ranging from noise absorption to vibration control, to seismic wave abatement. For this purpose, a plethora of complex architectures (including multi-phase materials) and multi-physics approaches have been proposed in the past, often involving difficulties in their practical realization. To address this issue, in this work we propose an easy-to-manufacture design able to open large, low frequency complete Lamb band gaps exploiting a suitable arrangement of masses and stiffnesses produced by cavities in a monolithic material. The performance of the designed structure is evaluated by numerical simulations and confirmed by Scanning Laser Doppler Vibrometer (SLDV) measurements on an isotropic polyvinyl chloride plate in which a square ring region of cross-like cavities is fabricated. The full wave field reconstruction clearly confirms the ability of even a limited number of unit cell rows of the proposed design to efficiently attenuate Lamb waves. In addition, numerical simulations show that the structure allows to shift of the central frequency of the BG through geometrical modifications. The design may be of interest for applications in which large BGs at low frequencies are required.
Highlights
One of the main problems facing physicists and engineers working in the field of metamaterials is to achieve vibration damping and control over large, low-frequency ranges
The article is organized as follows: first, we present extensive numerical simulations aimed at finding suitable plate configurations capable of nucleating large band gaps (BGs) within the optimal operative frequency range of the scanning laser Doppler vibrometer (SLDV) using finite element simulations (FEMs)
The results clearly show that waves with a frequency content falling outside the BG propagate through the phononic region reaching the monitoring point R without substantial attenuation as the number of cross-like cavities increases, while when the frequency content of the propagating waves falls inside the BG, the phononic crystal ring region inhibits the wave propagation so that the displacement at point R is much smaller as the number of cross-like cavities increases
Summary
One of the main problems facing physicists and engineers working in the field of metamaterials is to achieve vibration damping and control over large, low-frequency ranges. A non-exhaustive list of lowfrequency applications includes acoustic absorption, vibration shielding, subwavelength imaging, cloaking, etc (Craster and Guenneau, 2012; Deymier, 2013) With these applications in mind, a plethora of different architectures (including multiphase materials) and multiphysics approaches have been proposed in recent years (Bavencoffe et al, 2009; Pennec et al, 2010; Wang and Wang, 2013; Andreassen et al, 2015), but many involve considerable practical difficulties in their realization due to their inherent complexity. Several studies have considered and shown that filtering and waveguiding properties are achievable in plates with stubs, including biphase materials (Hsiao et al, 2007; Hsu and Wu, 2007; Wu et al, 2009, 2011; Oudich et al, 2011; Casadei et al, 2012) In these approaches, geometrical/physical complexity is often inevitable, leading to considerable complications in their practical realization. The calculated BGs are verified experimentally, and the direct observation of scattering phenomena below, within, and above the BGs is described
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