Interfacial acoustic waves in one-dimensional anisotropic phononic bicrystals with a symmetric unit cell

The paper is concerned with the interfacial acoustic waves localized at the internal boundary of two different perfectly bonded semi-infinite one-dimensional phononic crystals represented by periodically layered or functionally graded elastic structures. The unit cell is assumed symmetric relative to its midplane, whereas the constituent materials may be of arbitrary anisotropy. The issue of the maximum possible number of interfacial waves per full stop band of a phononic bicrystal is investigated. It is proved that, given a fixed tangential wavenumber, the lowest stop band admits at most one interfacial wave, while an upper stop band admits up to three interfacial waves. The results obtained for the case of generally anisotropic bicrystals are specialized for the case of a symmetric sagittal plane.

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Multifunctional One-dimensional Phononic Crystal Structures Exploiting Interfacial Acoustic Waves

MRS Proceedings ◽

10.1557/proc-1188-ll06-04 ◽

2009 ◽

Vol 1188 ◽

Author(s):

Albert C To ◽

Bong Jae Lee

Keyword(s):

Acoustic Waves ◽

Filter Design ◽

Phononic Crystal ◽

Stop Band ◽

Phononic Crystals ◽

Thermal Barrier ◽

Interfacial Wave ◽

Lateral Direction ◽

One Dimensional ◽

Wave Filter

AbstractThe present study demonstrates that interfacial acoustic waves can be excited at the interface between two phononic crystals. The interfacial wave existing between two phononic crystals is the counterpart of the surface electromagnetic wave existing between two photonic crystals. While past works on phononic crystals exploit the unique bandgap phenomenon in periodic structures, the present work employs the Bloch wave in the stop band to excite interfacial waves that propagate along the interface and decay away from the interface. As a result, the proposed structure can be used as a wave filter as well as a thermal barrier. In wave filter design, for instance, the incident mechanical wave energy can be guided by the interfacial wave to the lateral direction; thus, its propagation into the depth is inhibited. Similarly, in thermal barrier design, incident phonons can be coupled with the interfacial acoustic wave, and the heat will be localized and eventually dissipated at the interface between two phononic crystals. Consequently, the thermal conductivity in the direction normal to the layers can be greatly reduced. The advantage of using two phononic crystals is that the interfacial wave can be excited even at normal incidence, which is critical in many engineering applications. Since the proposed concept is based on a one-dimensional periodic structure, the analysis, design, and fabrication are relatively simple compared to other higher dimensional material designs.

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Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

Physical Review B ◽

10.1103/physrevb.100.184303 ◽

2019 ◽

Vol 100 (18) ◽

Cited By ~ 1

Author(s):

A. N. Darinskii ◽

A. L. Shuvalov

Keyword(s):

Acoustic Waves ◽

Surface Acoustic Waves ◽

Phononic Crystals ◽

Unit Cell ◽

One Dimensional

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Conformal Wireframe Nets for Trimmed Symmetric Unit Cells in Functionally Graded Lattice Materials

Applied Mechanics ◽

10.3390/applmech2010006 ◽

2021 ◽

Vol 2 (1) ◽

pp. 81-107

Author(s):

Eric Trudel ◽

Mostafa S. A. ElSayed

Keyword(s):

Computer Aided Design ◽

Functionally Graded ◽

Unit Cell ◽

Optimized Design ◽

Face Centered Cubic ◽

Lattice Structures ◽

One Dimensional ◽

Lattice Material ◽

Graded Lattice ◽

Novel Algorithm

Tessellating a periodic unit cell of lattice material to fill a design space in complex geometries has many challenges arising from their computer-aided design (CAD) modeling intricacy. A solution to this difficulty is the use of trimmed micro-truss lattice structures with a conformal net. This paper presents a novel algorithm for constructing conformal lattice net as wireframe of one-dimensional line segments suitable for Bravais cubic symmetric truss-based topologies. The novel algorithm is an excellent candidate when dealing with lattice structures using cubic, body-centered cubic (BCC), face-centered cubic (FCC), and/or diamond unit cell configurations. The wireframe structure is easily transferred into one-dimensional beam elements for microscale optimizations to obtain a functionally graded lattice material. It is shown that introduction of the lattice net resulted in a significant reduction in the mass of the optimized design.

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Axial guided wave characteristics in functionally graded one-dimensional hexagonal piezoelectric quasi-crystal cylinders

Mathematics and Mechanics of Solids ◽

10.1177/10812865211013458 ◽

2021 ◽

pp. 108128652110134

Author(s):

B. Zhang ◽

X.H. Wang ◽

L. Elmaimouni ◽

J.G. Yu ◽

X.M. Zhang

Keyword(s):

Coupling Effect ◽

Energy Conversion Efficiency ◽

Guided Wave ◽

Functionally Graded ◽

Phonon Modes ◽

One Dimensional ◽

Longitudinal Modes ◽

Wave Characteristics ◽

Piezoelectric Effects ◽

Hollow Cylinders

In one-dimensional hexagonal piezoelectric quasi-crystals, there exist the phonon–phason, electro–phonon, and electro–phason couplings. Therefore, the phonon–phason coupling and piezoelectric effects on axial guided wave characteristics in one-dimensional hexagonal functionally graded piezoelectric quasi-crystal (FGPQC) cylinders are investigated by utilizing the Legendre polynomial series method. The dispersion curves and cut-off frequencies are illustrated. Wave characteristics in three hollow cylinders with different quasi-periodic directions are comparatively studied. Some new wave phenomena are revealed: the phonon–phason coupling and piezoelectric effects on the longitudinal and torsional phonon modes ( N = 0) vary as the quasi-periodic direction changes; the phonon–phason coupling effect on flexural–torsional modes in the r-, z-FGPQC hollow cylinders, and on flexural–longitudinal modes in ϑ-FGPQC hollow cylinders increases as N increases. The corresponding results obtained in this work lay the theoretical foundation for the design and manufacture of piezoelectric transducers with high resolution and energy-conversion efficiency.

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Resonant excitation of acoustic waves in one-dimensional exciton-polariton systems

Physical Review A ◽

10.1103/physreva.100.043610 ◽

2019 ◽

Vol 100 (4) ◽

Author(s):

A. V. Yulin ◽

V. K. Kozin ◽

A. V. Nalitov ◽

I. A. Shelykh

Keyword(s):

Acoustic Waves ◽

Resonant Excitation ◽

One Dimensional

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Effect of Double Defects on Transmission Spectra of One-Dimensional Photonic Crystals

Materials Science Forum ◽

10.4028/www.scientific.net/msf.663-665.725 ◽

2010 ◽

Vol 663-665 ◽

pp. 725-728 ◽

Cited By ~ 1

Author(s):

Yuan Ming Huang ◽

Qing Lan Ma ◽

Bao Gai Zhai ◽

Yun Gao Cai

Keyword(s):

Photonic Crystals ◽

Band Gap ◽

Theoretical Calculations ◽

Stop Band ◽

Band Gaps ◽

Characteristic Matrix ◽

Frequency Range ◽

Defect Band ◽

One Dimensional ◽

The One

Considered the model of the one-dimensional photonic crystals (1-D PCs) with double defects, the refractive indexes (n2’, n3’ and n2’’, n3’’) of the double defects were 2.0, 4.0 and 4.0, 2.0 respectively. With parameter n2=1.5, n3=2.5, by theoretical calculations with characteristic matrix method, the results shown that for a certain number (14 was taken) of layers of the 1-D PCs, when the double defects abutted, there was a defect band gap in the stop band gap, while when the double defects separated, there occurred two defect band gaps in the stop band gap; besides, with the separation of the two defects, the transmittance of the double defect band gaps decreased gradually. In addition, in this progress, the frequency range of the stop band gap has a little increase from 0.092 to 0.095.

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One-dimensional acoustic waves in retarding structures with propagation velocity tending to zero

Acoustical Physics ◽

10.1134/1.1478121 ◽

2002 ◽

Vol 48 (3) ◽

pp. 347-352 ◽

Cited By ~ 28

Author(s):

M. A. Mironov ◽

V. V. Pislyakov

Keyword(s):

Acoustic Waves ◽

Propagation Velocity ◽

One Dimensional

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The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited

Journal of Applied Mechanics ◽

10.1115/1.1533805 ◽

2003 ◽

Vol 70 (3) ◽

pp. 359-363 ◽

Cited By ~ 40

Author(s):

S. Mukherjee ◽

Glaucio H. Paulino

Keyword(s):

Functionally Graded Materials ◽

Functionally Graded Material ◽

Correspondence Principle ◽

Functionally Graded ◽

Graded Materials ◽

One Dimensional ◽

Space And Time ◽

Graded Material ◽

Nonhomogeneous Materials ◽

Exponentially Graded

Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.

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