Vibration band gaps in double-vibrator pillared phononic crystal plate

Zhao, Haojiang; Guo, Hongwei; Gao, Mingxing; Liu, Rongqiang; Deng, Zongquan

doi:10.1063/1.4939484

Cited by 49 publications

(29 citation statements)

References 19 publications

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“…In order to investigate the vibration characteristics of the proposed elastic metamaterial plate, the band structures are calculated by using the FEM which has been proved to be an efficient method in previous works [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. For the calculation of the dispersion relations, an infinite periodic structure is considered with periodic boundary conditions applied on the interfaces among the adjacent unite cells according to the Bloch-Floquet theorem and the Bloch wave k is introduced.…”

Section: Methodsmentioning

confidence: 99%

The two-degree-of-freedom local resonance elastic metamaterial plate with broadband low-frequency bandgaps

et al. 2017

J. Phys. D: Appl. Phys.

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A theoretical model of a new type of two-degree-of-freedom local resonance mass-spring system with the resonator considering vertical and rotational vibration (the moment of inertia) is proposed to generate a negative effective mass over specific frequency ranges. Based on the theoretical analysis, a novel elastic metamaterial plate is designed. The flexural vibration band structures as well as the transmission spectrum of the metamaterial plate are investigated by using the finite element method. Subsequently, the formation mechanism of the band gaps is analyzed by studying the displacement field of the eigenmodes at the band gap edges. At last, the effects of the geometrical parameters on the flexural vibration band gaps (FVBGs) are studied and discussed in detail. The related results well confirm that the two-degree-of-freedom metamaterial shows negative mass density in two distinctive asymptotic regions, and the proposed elastic metamaterial plate has two FVBGs with the total width of 94.45 Hz below 200 Hz. The magnitude of torques introduced into the local resonance system can obviously affect the locations of the FVBGs. For the elastic metamaterial plate with thick local resonance lead plate and weak rubber is appropriate to obtain a lower gap, but the total width of the FVBGs becomes narrow. However, it does just the opposite for the condition with thin local resonance lead plate and strong rubber. For the double-side stubbed plate, it can enhance the coupling of the flexural traveling wave and the local resonance modes, which can greatly enlarge the bandwidths. The new working mechanism and the related calculation results of the designed structures would provide an effective way for elastic metamaterial plate to broaden the FVBGs at low frequencies, which has potential applications in low-frequency vibration and noise attenuation.

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Section: Methodsmentioning

confidence: 99%

The two-degree-of-freedom local resonance elastic metamaterial plate with broadband low-frequency bandgaps

et al. 2017

J. Phys. D: Appl. Phys.

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“…The lumped mass method [36,37] converges fast, but there are some difficulties in dealing with multi-field coupling problems. The FEM method [38][39][40] is a commonly used method in engineering with good applicability, wide application range, and good convergence. There are various kinds of mature commercial software, such as Comsol, ANSYS, etc., which facilitate the modeling and analysis of complex periodic structures.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

et al. 2019

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The differential quadrature method has been developed to calculate the elastic band gaps from the Bragg reflection mechanism in periodic structures efficiently and accurately. However, there have been no reports that this method has been successfully used to calculate the band gaps of locally resonant structures. This is because, in the process of using this method to calculate the band gaps of locally resonant structures, the non-linear term of frequency exists in the matrix equation, which makes it impossible to solve the dispersion relationship by using the conventional matrix-partitioning method. Hence, an accurate and efficient numerical method is proposed to calculate the flexural band gap of a locally resonant beam, with the aim of improving the calculation accuracy and computational efficiency. The proposed method is based on the differential quadrature method, an unconventional matrix-partitioning method, and a variable substitution method. A convergence study and validation indicate that the method has a fast convergence rate and good accuracy. In addition, compared with the plane wave expansion method and the finite element method, the present method demonstrates high accuracy and computational efficiency. Moreover, the parametric analysis shows that the width of the 1st band gap can be widened by increasing the mass ratio or the stiffness ratio or decreasing the lattice constant. One can decrease the lower edge of the 1st band gap by increasing the mass ratio or decreasing the stiffness ratio. The band gap frequency range calculated by the Timoshenko beam theory is lower than that calculated by the Euler-Bernoulli beam theory. The research results in this paper may provide a reference for the vibration reduction of beams in mechanical or civil engineering fields.

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“…However, it has been a challenging task due to the long wavelength and weak attenuation of the low-frequency waves. In the past years, many LRPCs were proposed to obtain bandgaps in low frequency range or broaden bandgaps in the low frequency range [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. More recently, the propagation of Lamb waves (elastic waves) in phononic crystal plates, which is based on a local resonance mechanism, has attracted attention due to their potential applications in filters, resonators, waveguides, and for vibration insulation.…”

Section: Introductionmentioning

confidence: 99%

Metal-Matrix Embedded Phononic Crystals

Li¹,

Dou²,

Niu³

2019

Photonic Crystals - A Glimpse of the Current Research Trends

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Metal-matrix embedded phononic crystals (MMEPCs) can be applied for noise and vibration reduction. Metal-matrix embedded phononic crystals (MMEPCs) consisting of double-sided stubs (single "hard" stubs/composite stubs) were introduced. The introduced MMEPCs are deposited on a twodimensional locally resonant phononic crystal plate that consists of an array of rubber fillers embedded in a steel plate. The lower frequency complete bandgap will be produced in the MMEPCs with composite stubs by decoupling the spring-mass system of the resonator by means of the rubber filler. Then, the out-of-plane bandgap and the in-plane bandgap can be adjusted into the same lowest frequency range by the composite stubs. The broad complete bandgap will be produced in the metal-matrix embedded phononic crystals with single "hard" stubs by producing new kinds of resonance modes (in-plane and out-of-plane analogous-rigid modes) by introducing the single "hard" stubs, and then the out-of-plane bandgap and the in-plane bandgap can be broadened into the same frequency range by the single "hard" stubs. The proposed MMEPCs can be used for noise and vibration reduction.Keywords: metal-matrix embedded phononic crystals, lower frequency complete bandgap, broad complete bandgap, forming mechanisms of the bandgap, noise, vibration reduction Photonic Crystals -A Glimpse of the Current Research Trends

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Vibration band gaps in double-vibrator pillared phononic crystal plate

Cited by 49 publications

References 19 publications

The two-degree-of-freedom local resonance elastic metamaterial plate with broadband low-frequency bandgaps

The two-degree-of-freedom local resonance elastic metamaterial plate with broadband low-frequency bandgaps

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

Metal-Matrix Embedded Phononic Crystals

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