Analysis of flexural wave bandgaps in periodic plate structures using differential quadrature element method

Cheng, Zhibao; Xu, Yong; Zhang, L.L.

doi:10.1016/j.ijmecsci.2015.06.014

Cited by 44 publications

(17 citation statements)

References 53 publications

(59 reference statements)

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“…11 shows the LBF, UBF and WAZ changing with the periodic constant. It can be seen that the LBF, UBF and WAZ decrease drastically as the periodic constant increases, which implies that the DAZ 13 will disappear when the periodic constant is sufficiently large. The reason is that the wave scattering effect of the inclusion is gradually reduced as the periodic constant increases.…”

Section: Effect Of the Initial Stress On The Daz And The Attenuation mentioning

confidence: 99%

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Attenuation zones of initially stressed periodic Mindlin plates on an elastic foundation

Liu

Shi

2016

International Journal of Mechanical Sciences

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A new numerical approach based on the weak form quadrature element method (WFQEM) is proposed to study attenuation zones of initially stressed periodic Mindlin plates on an elastic foundation.The proposed method is validated by the results available in the previous studies of initially stressed homogeneous plates on elastic foundations. A comprehensive parametric study is conducted to highlight the effects of initial stress, geometric parameters and elastic foundation on the attenuation zones. The resultsshow that the compressive initial stress shifts the attenuation zones to lower frequencies and enhances the attenuation of waves in the attenuation zones, while the tensile initial stress shifts the attenuation zones to higher frequencies and weakens the attenuation of waves in the attenuation zones. The elastic foundation shifts the attenuation zones to higher frequencies and narrows the width of the attenuation zones. In addition, wave propagation and attenuation in a periodic Mindlin plate with finite unit cells on an elastic foundation are examined. The results achieved in this paper are very useful for the design and application of periodic plates in vibration reduction in most of engineering fields.

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Section: Effect Of the Initial Stress On The Daz And The Attenuation mentioning

confidence: 99%

“…Further, Cheng et al [13] extended the DQEM in the study of the AZs for flexural waves in a plate with periodic piezoelectric patches, in which the detailed solution procedure with the DQEM is presented.…”

Section: Introductionmentioning

confidence: 99%

Attenuation zones of initially stressed periodic Mindlin plates on an elastic foundation

Liu

Shi

2016

International Journal of Mechanical Sciences

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“…Bloch‐Floquet theory describes the wave function of a particle in an infinite periodic medium, such as a crystal, in wave functions at the reciprocal space vectors for a Bravais lattice . The theory was originally developed to solve wavelike partial differential equations in the physical sciences.…”

Section: Dispersion Theory For Periodic Foundationmentioning

confidence: 99%

Composite periodic foundation and its application for seismic isolation

Cheng

Shi

2017

Earthq Engng Struct Dyn

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Summary This paper proposes a novel multidimensional composite periodic foundation for seismic isolation. The composite periodic foundation achieves multidimensional attenuation by innovative arrangement of periodic structures and taking advantage of the directional attenuation zone of periodic structures. Directional attenuation zones of periodic structures are derived for the in‐plane wave, and the impact of geometrical parameters of the periodic structure on the characteristics of the directional attenuation zones is studied. The effectiveness of the proposed composite periodic foundation is demonstrated through application in seismic isolation for nuclear power plant structures. Harmonic analysis and time history analysis results show that the proposed composite periodic foundation with low‐frequency directional attenuation zones can effectively reduce vibrations of the upper structure in both horizontal and vertical directions.

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“…There are two formation mechanisms of the elastic band gap in PCs: one is the Bragg scattering mechanism [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], and the other is the locally resonant mechanism. The wave length corresponding to the elastic band gap formed by Bragg scattering is generally equal to the lattice size or lattice constant, which restricts its application in engineering practice.…”

Section: Introductionmentioning

confidence: 99%

“…It has strong convergence and high precision. To the authors' knowledge, the DQM was only applied to solve the elastic wave band gap of a beam or plate structure with the Bragg scattering mechanism [8,9]. However, the Bloch boundary conditions for locally resonant structures lead to nonlinear fundamental equations when using DQM, which causes difficulties in solving.…”

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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Analysis of flexural wave bandgaps in periodic plate structures using differential quadrature element method

Cited by 44 publications

References 53 publications

Attenuation zones of initially stressed periodic Mindlin plates on an elastic foundation

Attenuation zones of initially stressed periodic Mindlin plates on an elastic foundation

Composite periodic foundation and its application for seismic isolation

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

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