Vibration band-gap properties of three-dimensional Kagome lattices using the spectral element method

Wu, Zhijing; Li, Fengming; Zhang, Chuanzeng

doi:10.1016/j.jsv.2014.12.038

Cited by 70 publications

(15 citation statements)

References 24 publications

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“…Based on theoretical and numerical methods, the existence of phononic band gaps has been predicted in lattice topologies 8,9 , undulated lattices 10 and three-dimensional lattices 9,11,12 . The size and position of phononic band gaps in cellular solids can be controlled via the topology 13 and dimension 14 of the underlying unit cell.…”

Section: 2mentioning

confidence: 99%

“…Furthermore, hybridization gaps are caused by coupling of the rigid-body resonances of individual inclusions as well as the propagating mode in the embedding medium and do not need a periodic arrangement of inclusions 3,7 . Another mechanism appears only in systems in which masses are elastically bonded: in such a mechanism the resonant modes of the masses interact via the elastic bonding and passbands are generated Based on theoretical and numerical methods, the existence of phononic band gaps has been predicted in lattice topologies 8,9 , undulated lattices 10 and three-dimensional lattices 9,11,12 . The size and position of phononic band gaps in cellular solids can be controlled via the topology 13 and dimension 14 of the underlying unit cell.…”

mentioning

confidence: 99%

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Single phase 3D phononic band gap material

Warmuth

Wormser

Körner

2017

Sci Rep

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Phononic band gap materials are capable of prohibiting the propagation of mechanical waves in certain frequency ranges. Band gaps are produced by combining different phases with different properties within one material. In this paper, we present a novel cellular material consisting of only one phase with a phononic band gap. Different phases are modelled by lattice structure design based on eigenmode analysis. Test samples are built from a titanium alloy using selective electron beam melting. For the first time, the predicted phononic band gaps via FEM simulation are experimentally verified. In addition, it is shown how the position and extension of the band gaps can be tuned by utilizing knowledge-based design.Materials with complete phononic band gaps show frequency intervals in which the propagation of mechanical waves is not possible for any direction 1 . A lot of studies have been dedicated to phononic crystal systems with periodic variation of density and large mismatches in wave speed periodically modulated on a length scale comparable to the desired wavelength based on multi-phase systems [1][2][3][4] . We present a novel approach of designing the unit cell of a single phase three-dimensional cellular structure leading to complete and tunable phononic band gaps. Additive manufacturing is used to fabricate samples and verify the numerical predictions. This, in turn, opens completely new ways to adjust the vibrational and damping properties of structural components.Materials with phononic band gaps are either phononic crystals or acoustic metamaterials. Croënne et al. 5defined phononic crystals as systems in which the periodic arrangement of scatterers in a matrix is responsible for the emergence of phononic band gaps. Acoustic metamaterials, however, rely on the characteristics of the single inclusions inside the medium 5 . Different phononic band gap formation mechanisms have been described in literature 5 . The most common one relies on Bragg scattering of the waves in phononic crystals at the periodic inclusions and their destructive interference, hence they are called Bragg gaps 6 . Furthermore, hybridization gaps are caused by coupling of the rigid-body resonances of individual inclusions as well as the propagating mode in the embedding medium and do not need a periodic arrangement of inclusions 3,7 . Another mechanism appears only in systems in which masses are elastically bonded: in such a mechanism the resonant modes of the masses interact via the elastic bonding and passbands are generated Based on theoretical and numerical methods, the existence of phononic band gaps has been predicted in lattice topologies 8,9 , undulated lattices 10 and three-dimensional lattices 9,11,12 . The size and position of phononic band gaps in cellular solids can be controlled via the topology 13 and dimension 14 of the underlying unit cell. Apart from the chosen geometry 9, 15 , the slenderness ratio of the struts 8 and the angle between the struts 16 were identified as key parameters for controlling the band structu...

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Section: 2mentioning

confidence: 99%

mentioning

confidence: 99%

Single phase 3D phononic band gap material

Warmuth

Wormser

Körner

2017

Sci Rep

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“…The spectral element method (SEM) is a highly precise and efficient frequency-domain solution method where the spectral element equation is formulated in the frequencydomain and solved by using the spectral analysis method [9][10][11]. The procedure of the SEM is similar to that of the conventional finite element method.…”

Section: Introductionmentioning

confidence: 99%

Study on Transmission Characteristics of Vertical Rail Vibrations in Ballast Track

Sheng

Zhao

Wang

et al. 2017

Mathematical Problems in Engineering

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A plane half-track model and a periodic track-substructure model are established. The spectral element method and spectral transfer matrix method are developed and applied to investigate the track decay rate (TDR) and transmission rate (TR) of the vertical rail vibrations, which can reflect the transmission characteristics in the longitudinal and downward directions, respectively. Furthermore, the effects of different track parameters on TDR and TR are investigated. The results show that the antiresonance frequency of the rail and the out-of-phase resonance frequency of the rail and sleeper form the boundary frequencies of the highattenuation zone for longwise vibration transmission, where the vibration absorption of the sleeper is significant. The downward transmissibility of vertical rail vibrations is greatest around the antiresonance frequency of the rail. Vertical rail vibrations are primarily transmitted in the downward direction at low frequencies, while they are mainly transmitted along the rail at high frequencies. Stiffer rail pads can make more vibrations transmitted downwards to the sleeper above the antiresonance frequency of the rail, while the changes of other track parameters have different effects on the transmission characteristics. Additionally, a field measurement is performed for verification, and the simulations are well consistent with measurements.

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“…beams and the vibration properties and band structure of their unit cells are investigated. In term of analysis this paper is mainly focused on Frequency Response Functions (FRF) and spectral analysis to study the dynamic behaviour of the structures [35,36,37]. Aynaou et al [38] performed a theoretical investigation on acoustic wave propagation of onedimensional phononic band gap structures made of slender tube loops pasted together with slender tubes of finite length according to a Fibonacci sequence.…”

Section: Introductionmentioning

confidence: 99%

Spectral analysis and structural response of periodic and quasi-periodic beams

Timorian

Petrone

Rosa

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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Periodic structures have found a big interest in engineering applications because they introduce frequency band effects, due to the impedance mismatch generated by periodic discontinuities in the geometry, material, or boundary conditions, which can improve the vibroacoustic performances. However, the presence of defects or irregularity in the structure leads to a partial lost of regular periodicity (called quasi-periodic structure) that can have a noticeable impact on the vibrational and/or acoustic behavior of the elastic structure. The irregularity can be tailored to have impact on dynamical behavior. In the present paper, numerical studies on the vibrational analysis of one-dimensional finite, periodic, and quasi-periodic structures are presented. The contents deal with the finite element models of beams focused on the spectral analysis and the damped forced responses. The quasi-periodicity is defined by invoking the Fibonacci sequence for building the assigned variations (geometry and material) along the span of finite element model. Similarly, the same span is used as a super unit cell with Floquet–Bloch conditions waves for analyzing the infinite periodic systems. Considering both longitudinal and flexural elastic waves, the frequency ranges corresponding to band gaps are investigated. The wave characteristics in quasi-periodic beams, present some elements of novelty and could be considered for designing structural filters and controlling the properties of elastic waves.

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Vibration band-gap properties of three-dimensional Kagome lattices using the spectral element method

Cited by 70 publications

References 24 publications

Single phase 3D phononic band gap material

Single phase 3D phononic band gap material

Study on Transmission Characteristics of Vertical Rail Vibrations in Ballast Track

Spectral analysis and structural response of periodic and quasi-periodic beams

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