Three-dimensional resonating metamaterials for low-frequency vibration attenuation

Elmadih, W.; Chronopoulos, D.; Syam, W.P.; Maskery, I.; Meng, H.; Leach, R.K.

Abstract

Recent advances in additive manufacturing have enabled fabrication of phononic crystals and metamaterials which exhibit spectral gaps, or stopbands, in which the propagation of elastic waves is prohibited by Bragg scattering or local resonance effects. Due to the high level of design freedom available to additive manufacturing, the propagation properties of the elastic waves in metamaterials are tunable through design of the periodic cell. In this paper, we outline a new design approach for metamaterials incorporating internal resonators, and provide numerical and experimental evidence that the stopband exists over the irreducible Brillouin zone of the unit cell of the metamaterial (i.e. is a three-dimensional stopband). The targeted stopband covers a much lower frequency range than what can be realised through Bragg scattering alone. Metamaterials have the ability to provide (a) lower frequency stopbands than Bragg-type phononic crystals within the same design volume, and/or (b) comparable stopband frequencies with reduced unit cell dimensions. We also demonstrate that the stopband frequency range of the metamaterial can be tuned through modification of the metamaterial design. Applications for such metamaterials include aerospace and transport components, as well as precision engineering components such as vibration-suppressing platforms, supports for rotary components, machine tool mounts and metrology frames. Phononic crystals (PCs) are engineered materials designed to control elastic wave propagation. PCs generally rely on high impedance mismatches within their structural periodicity to form Bragg-type stopbands that exist due to the destructive interference between transmitted and reflected waves. The presence of destructive interference prevents specific wave types from propagating. Kushwaha et al. 1 presented the first comprehensive calculation of acoustic bands in a structure of periodic solids embedded in an elastic background. James et al. 2 used a periodic array of polymer plates submerged in water and provided experimental realisation of one-dimensional (1D) and two-dimensional (2D) PCs. Montero de Espinosa et al. 3 used aluminium alloy plates with cylindrical holes filled with mercury to generate 2D ultrasonic stopbands. Tanaka et al. 4 studied the homogeneity of PCs in the perpendicular direction to the direction of propogation, and classified PCs into bulk PCs and slab PCs. Research on the design, manufacturing and testing of PCs has mainly focused on 1D and 2D PCs 5-14 , although recently, the research has been extended to include 3D PCs 15-22. Lucklum et al. 23 discussed the manufacturing challenges of 3D PCs and showed that additive manufacturing (AM) has the fabrication capabilities required for the realisation of geometrically complex 3D PCs 24-27. There are a wide variety of AM technologies that may be used to manufacture PC materials, such as laser powder bed fusion (LPBF), photo-polymerization, stereolithography and inkjet printing 28-31. Although differing in the manufacturing resolution (the thickness of the build layer), materials, design constraints and cost, these AM technologies create 3D parts from a CAD model. The creation of the 3D parts is usually carried out layer by layer, and the thickness of the deposited layers, as well as the effects of post-processing, determine the geometrical quality of the created 3D parts 32,33. Despite the benefits of the recent ability to manufacture PCs with AM, their effectiveness at low-frequencies is limited due to the dependency of the resulting stopbands on Bragg scattering. Bragg scattering occurs due to destructive interference of the propagating waves with the in-phase reflected waves, which occurs when the wavelengths of the reflected and propagating waves are similar. The reflection occurs due to the difference in the impedance (e.g. local density) of the PC. For the in-phase reflection to occur, the Bragg law has to be satisfied 34 , which is highly dependent on the cell size of the PC. Bragg scattering starts to occur when the wavelength is approximately equal to twice the cell size of the PC 34 ; around a normalised frequency (the quotient of cell size and wavelength) of 0.5. Thus, there is a limiting dependency on the size of the unit cell of the PCs to form stopbands by Bragg scattering. As a result of this dependency, unrealistic cell sizes need to be employed to satisfy the Bragg law at low-frequencies. It is possible to form stopbands below the lowest Bragg limit using metamaterials with periodically arranged local resonators. The stopbands in these metamaterials are formed by absorbing wave energy around the resonant frequency 35-42. The benefits of resonator-based metamaterials include increased design freedom and the flexibility to obtain stopbands in structures of higher periodicity within a fixed design volume compared to conventional PCs. Thus, resonator-based metamaterials provide better-defined stopbands. Research on locally resonant metamaterials includes the work of Liu et al. 42 , who first developed a

Citation

Elmadih, W., Chronopoulos, D., Syam, W., Maskery, I., Meng, H., & Leach, R. (2019). Three-dimensional resonating metamaterials for low-frequency vibration attenuation. Scientific Reports, 9(1), Article 11503. https://doi.org/10.1038/s41598-019-47644-0

• Journal Article Type: Article
• Acceptance Date: Jul 15, 2019
• Online Publication Date: Aug 8, 2019
• Publication Date: 2019-12
• Deposit Date: Jul 30, 2019
• Publicly Available Date: Aug 12, 2019
• Journal: Scientific Reports
• Electronic ISSN: 2045-2322
• Publisher: Nature Publishing Group
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Issue: 1
• Article Number: 11503
• DOI: https://doi.org/10.1038/s41598-019-47644-0
• Keywords: Multidisciplinary
• Public URL: https://nottingham-repository.worktribe.com/output/2355557
• Publisher URL: https://www.nature.com/articles/s41598-019-47644-0
• Additional Information: Received: 7 April 2019; Accepted: 15 July 2019; First Online: 8 August 2019; : The authors declare no competing interests.