The Band Gaps of Plate-Mode Waves in One-Dimensional Piezoelectric Composite Plates: Polarizations and Boundary Conditions

2007 ◽  
Vol 54 (7) ◽  
pp. 1430-1436 ◽  
Author(s):  
Xin-Ye Zou ◽  
Qian Chen ◽  
Jian-chun Cheng
Keyword(s):  
Boundary Conditions ◽  
Composite Plates ◽  
Band Gaps ◽  
Piezoelectric Composite ◽  
One Dimensional

Controllable acoustic rectification in one-dimensional piezoelectric composite plates

2013 ◽  
Vol 114 (16) ◽  
pp. 164504 ◽  
Author(s):  
Xin-Ye Zou ◽  
Bin Liang ◽  
Ying Yuan ◽  
Xue-Feng Zhu ◽  
Jian-Chun Cheng
Keyword(s):  
Composite Plates ◽  
Piezoelectric Composite ◽  
One Dimensional

scholarly journals Creating the Coupled Band Gaps in Piezoelectric Composite Plates by Interconnected Electric Impedance

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1656 ◽  
Author(s):  
Lin Li ◽  
Zhou Jiang ◽  
Yu Fan ◽  
Jun Li
Keyword(s):  
Band Gap ◽  
Piezoelectric Materials ◽  
Composite Plates ◽  
Forced Response ◽  
Band Gaps ◽  
Piezoelectric Composite ◽  
Flexural Wave ◽  
Response Analysis ◽  
Flexural Waves ◽  
Single Wave

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electric and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electric wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). The features of the coupled band gap are validated by a forced response analysis. We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to adaptively create band gaps.

Coupled Band Gaps in the Piezoelectric Composite Plate With Interconnected Electric Impedance

2018 ◽  
Author(s):  
Lin Li ◽  
Zhou Jiang ◽  
Yu Fan ◽  
Jun Li
Keyword(s):  
Band Gap ◽  
Piezoelectric Materials ◽  
Composite Plates ◽  
Band Gaps ◽  
Piezoelectric Composite ◽  
Flexural Wave ◽  
Flexural Waves ◽  
Single Wave ◽  
Electric Parameters ◽  
Sub Wavelength

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electrical and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electrical wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to create sub-wavelength band gaps.

Band Gaps of Lamb Waves Propagating in One-Dimensional Different Quasi-Periodic Composite Thin Plates

2012 ◽  
Vol 160 ◽  
pp. 175-179
Author(s):  
Jian Gao ◽  
Min Zhao ◽  
Ya Zhuo Xie ◽  
Xing Gan Zhang
Keyword(s):  
Lamb Waves ◽  
Plate Thickness ◽  
Physical Property ◽  
Composite Plates ◽  
Band Gaps ◽  
Thin Plates ◽  
Periodic Sequences ◽  
One Dimensional ◽  
Periodic Composite ◽  
Periodic Models

We present a comparative study on band-gap structures of Lamb waves propagating in one-dimensional quasi-periodic composite thin plates, which are composed of different quasi-periodic models such as Cantor, Fibonacci, Thue-Morse, and Double periodic sequences, respectively. The transmitted power spectra (TPS) of the transient Lamb waves propagating in composite plates is calculated numerically by employing the finite element method. By comparing among TPS in different plates with the different ratios of the plate thickness to the lattice spacing, it is found that different quasi-periodic models present different behavior of the split-up of band gaps. Our works are significant not only for understanding intrinsic physical property of the quasi-periodic sequences, but also for designing the special structures of quasi-periodic arrays to adjust the width of band gaps and the frequency ranges of phononic crystals in applications.

LAMB WAVE TRANSMISSION THROUGH ONE-DIMENSIONAL THREE-COMPONENT FIBONACCI COMPOSITE PLATES

2010 ◽  
Vol 24 (02) ◽  
pp. 161-167 ◽  
Author(s):  
JIU-JIU CHEN ◽  
QIONG WANG ◽  
XU HAN
Keyword(s):  
Lamb Wave ◽  
Composite Plates ◽  
Band Gaps ◽  
Transmission Spectra ◽  
Lattice Period ◽  
The Finite Element Method ◽  
Filling Fraction ◽  
One Dimensional ◽  
Two Component ◽  
Wave Modes

Using the finite element method, we have calculated the transmission spectra of Lamb wave modes which propagate in one-dimensional three-component Fibonacci quasiperiodic composite plates made of three different materials, and analyzed the influence of filling fraction, the ratio of the thickness of the plates to the lattice period and especially the number of generations on the band gaps of Lamb wave modes. The band gap splitting depends on the number of generations which is different from those of one-dimensional two-component Fibonacci composite plates. Engineering band gaps can be obtained by turning different parameters and the number of generations.

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

scholarly journals Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Przemysław Kościk ◽  
Arkadiusz Kuroś ◽  
Adam Pieprzycki ◽  
Tomasz Sowiński
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Pair Correlation ◽  
Contact Interactions ◽  
One Dimensional ◽  
Particle Correlations ◽  
Variational Scheme ◽  
Full Control ◽  
Arbitrary Shapes

AbstractWe derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations have two-body nature. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions. We show its efficiency in a whole range of intermediate interactions for different external potentials. Our results manifest that for generic non-parabolic potentials mutual correlations forced by interactions cannot be captured by distance-dependent functions.

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