Ultrasonic guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) are studied in this paper. A semi-analytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the long dimension of the plate is used. The method is applicable to an arbitrary number of layers of anisotropic properties and is similar to that used earlier to study guided waves in layered anisotropic plates of infinite width. Numerical results are presented for acoustic phonon modes of quasi-one-dimensional (QID) wires. For homogeneous wires, these agree well with recently reported results for dispersion of these modes.
Issue Section:
Technical Papers
1.
Nayfeh, A. H., 1995, Wave Propagation in Layered Anisotropic Media with Applications to Composites, Elsevier, Amsterdam, The Netherlands.
2.
Datta, S. K., 2000, “Wave Propagation in Composite Plates and Shells,” Comprehensive Composite Materials, Vol. 1, Chapter 18, T.-W. Chou, ed., Elsevier, Amsterdam, The Netherlands, pp. 511–558.
3.
Rose, J. L., 1999, Ultrasonic Waves in Solid Media, Cambridge Press.
4.
Chimenti
, D. E.
, 1997
, “Guided Waves in Plates and Their Use in Material Characterization
,” Appl. Mech. Rev.
, 50
, pp. 247
–284
.5.
SeGi
, Y.
, Kim
, K. W.
, Stroscio
, M. A.
, Iafrate
, G. J.
, and Ballato
, A.
, 1994
, “Electron-Acoustic-Phonon Scattering Rates in Rectangular Quantum Wires
,” Phys. Rev. B
, 50
, pp. 1733
–1738
.6.
Datta, S. K., Dunn, M. L., Sesselman, R., and Niklasson, J., 1999, “Mechanical Behavior and Ultrasonic Characterization of Ductile/Brittle Layered Material Systems,” Proc., 17th Symposium on Energy Engineering Sciences, B. Armaly, ed., Argonne National Laboratory, Argonne, IL, pp. 82–89.
7.
Niklasson, A. J., and Datta, S. K., 2000, “On the Modeling of Guided Waves in Plates with Superconducting Layers,” Review of Progress in Quantitative Nondestructive Evaluation, Vol. 19, D. O. Thompson and D. E. Chimenti, eds., American Institute of Physics, Melville, NY.
8.
Niklasson
, A. J.
, Datta
, S. K.
, and Dunn
, M. L.
, 2000
, “On Approximating Guided Waves in Plates with Thin Anisotropic Coatings by Means of Effective Boundary Conditions
,” J. Acoust. Soc. Am.
, 108
, pp. 924
–933
.9.
Niklasson
, A. J.
, Datta
, S. K.
, and Dunn
, M. L.
, 2000
, “On Ultrasonic Guided Waves in a Thin Anisotropic Layer Lying between Isotropic Layers
,” J. Acoust. Soc. Am.
, 108
, pp. 2005
–2011
.10.
Hernandez
, C. M.
, Murray
, T. W.
, and Krishnaswamy
, S.
, 2002
, “Photoacoustic Characterization of the Mechanical Properties of Thin Films
,” Appl. Phys. Lett.
, 80
, pp. 691
–693
.11.
Matsuda
, Y.
, Richardson
, C. J.
, and Spicer
, J. B.
, 2001
, “Spectral Compression of Ultrafast Acoustic Transients in Thin Films for Enhanced detectability
,” Appl. Phys. Lett.
, 79
, pp. 2288
–2290
.12.
Merlin
, R.
, 1997
, “Generating Coherent THz Phonons with Light Pulses
,” Solid State Commun.
, 102
, pp. 207
–220
.13.
Aalami
, B.
, 1973
, “Waves in Prismatic Guides of Arbitrary Cross Section
,” ASME J. Appl. Mech.
, 40
, pp. 1067
–1072
.14.
Taweel
, H.
, Dong
, S. B.
, and Kazic
, M.
, 2000
, “Wave Reflection from the Free End of a Cylinder with Arbitrary Cross-Section
,” Int. J. Solids Struct.
, 37
, pp. 1701
–1726
.15.
Datta
, S. K.
, Shah
, A. H.
, Bratton
, R. L.
, and Chakraborty
, T.
, 1988
, “Wave Propagation in Laminated Composite Plates
,” J. Acoust. Soc. Am.
, 83
, pp. 2020
–2026
.16.
Karunasena
, W.
, Shah
, A. H.
, and Datta
, S. K.
, 1991
, “Wave Propagation in a Multilayered Cross-ply Composite Plate
,” ASME J. Appl. Mech.
, 58
, pp. 1028
–1032
.17.
Shull
, P. J.
, Chimenti
, D. E.
, and Datta
, S. K.
, 1994
, “Elastic Guided Waves and the Floquet Concept in Periodically Layered Plates
,” J. Acoust. Soc. Am.
, 95
, pp. 99
–108
.18.
Datta
, S. K.
, Shah
, A. H.
, and Karunasena
, W.
, 1999
, “Ultrasonic Waves and Material and Defect Characterization in Composite Plates
,” Mechanics of Composite Materials and Structures
, 6
, pp. 285
–300
.19.
Nishiguchi
, N.
, Ando
, Y.
, and Wyburne
, M. N.
, 1997
, “Acoustic Phonon Modes of Rectangular Quantum Wires
,” J. Phys.: Condens. Matter
, 9
, pp. 5751
–5764
.20.
Visscher
, W. M.
, Migliori
, A.
, Bell
, T. M.
, and Reinert
, R. A.
, 1991
, “On The Normal-Modes of Free-Vibration of Homogenous and Anisotropic Elastic Objects
,” J. Acoust. Soc. Am.
, 90
, pp. 2154
–2164
.21.
Kynch
, G. J.
, 1957
, “The Fundamental Modes of Vibration of Uniform Beams for Medium Wavelengths
,” Br. J. Appl. Phys.
, 8
, pp. 64
–73
.22.
Nigro
, N. J.
, 1966
, “Steady-state Wave Propagation in Infinite Bars of Noncircular Cross Section
,” J. Acoust. Soc. Am.
, 40
, pp. 1501
–1508
.23.
Fraser
, W. B.
, 1969
, “Stress Wave Propagation in Rectangular Bars
,” Int. J. Solids Struct.
, 5
, pp. 379
–397
.24.
Mukdadi, O. M., Desai, Y. M., Datta, S. K., Shah, A. H., and Niklasson, A. J., 2001, “Elastic Guided Waves in a Layered Plate with Rectangular Cross Section,” submitted to J. Acoust. Soc. Am.
25.
Schwab
, K.
, Fon
, W.
, Henriksen
, E.
, Worlock
, J. M.
, and Roukes
, M. L.
, 2000
, “Quantized Thermal Conductance: Measurements in Nanostructures
,” Physica B
, 280
, pp. 458
–459
.26.
Vogelgesang
, R.
, and Grimsditch
, M.
, 2000
, “The Elastic Constants of Single Crystal β-Si3N4,
” Appl. Phys. Lett.
, 76
, pp. 982
–984
.27.
Adachi
, S.
, 1985
, “GaAs, AlAs, and AlxGa1−xAs: Material parameters for use in research and device applications
,” J. Appl. Phys.
, 58
, pp. R1–R28
R1–R28
.Copyright © 2002
by ASME
You do not currently have access to this content.
