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TECHNICAL PAPERS

Calculation of the Response of a Composite Plate to Localized Dynamic Surface Loads Using a New Wave Number Integral Method

[+] Author and Article Information
Sauvik Banerjee

Mechanical and Aerospace Engineering Department, University of California, Los Angeles, CA 90095-1597 e-mail: sauvik@ucla.edu

William Prosser

Nondestructive Evaluation Branch, NASA Langley Research Center, MS231, Hampton, VA 23681-0001e-mail: w.h.prosser@larc.nasa.gov

Ajit Mal

Mechanical and Aerospace Engineering Department, University of California, Los Angeles, CA 90095-1597e-mail: ajit@ucla.edu

J. Appl. Mech 72(1), 18-24 (Feb 01, 2005) (7 pages) doi:10.1115/1.1828064 History: Received May 12, 2003; Revised July 07, 2004; Online February 01, 2005
Copyright © 2005 by ASME
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References

Achenbach, J. D., 1978, Wave Propagation in Elastic Solids, North-Holland, New York.
Nayfeh, A. H., 1995, Wave Propagation in Layered Anisotropic Media: With Applications to Composites, Elsevier Science, Amsterdam.
Rose, J. L., 1999, Ultrasonic Waves in Solid Media, Cambridge University Press, New York.
Kundu,  T., and Mal,  A. K., 1985, “Elastic Waves in a Multilayered Solid Due to a Dislocation Source,” Wave Motion, 7, pp. 459–471.
Guo,  D., Mal,  A. K., and Ono,  K., 1996, “Wave Theory of Acoustic Emission in Composite Laminates,” J. Acoust. Emiss., 14, S19–S46.
Mal,  A. K., 1988, “Wave Propagation in Layered Composite Laminates Under Periodic Surface Loads,” Wave Motion, 10, pp. 257–266.
Mal,  A. K., and Lih,  S. S., 1992, “Elastodynamic Response of a Unidirectional Composite Laminate to Concentrated Surface Loads, Parts I & II,” ASME J. Appl. Mech., 55, pp. 878–892.
Lih,  S. S., and Mal,  A. K., 1996, “Response of Multilayered Composite Laminates to Dynamic Surface Loads,” Composites, Part B, 27B, pp. 633–641.
Reddy,  J. N., 1984, “A Simple Higher-Order Theory for Laminated Composite Plates,” ASME J. Appl. Mech., 51, pp. 745–752.
Lih,  S. S., and Mal,  A. K., 1995, “On the Accuracy of Approximate Plate Theories for Wave Field Calculations in Composite Laminates,” Wave Motion, 21, pp. 17–34.
Chimenti,  D. E., 1997, “Guided Waves in Plates and Their Use in Material Characterization,” Appl. Mech. Rev., 50, pp. 247–284.
Abrate, S., 1998, Impact on Composite Structures, Cambridge University Press, New York.
Xu,  P. C., and Mal,  A. K., 1985, “An Adaptive Integration Scheme for Irregularly Oscillating Functions,” Wave Motion, 7, pp. 235–243.
Dravinski,  M., and Mossessian,  T. K., 1988, “On the Evaluation of the Green’s Functions for Harmonic Line Loads in a Viscoelastic Half-Space,” Int. J. Numer. Methods Eng., 26, pp. 823–841.
Gary,  J., and Hamstad,  M., 1994, “On the Far-Field Structure of Waves Generated by a Pencil Break on a Thin Plate,” J. Acoust. Emiss., 12(3–4), pp. 157–170.
Hamstad,  M. A., Gary,  J., and O’Gallagher,  A., 1996, “Far-Field Acoustic Emission Waves by Three-Dimensional Finite Element Modeling of Pencil Breaks on a Thick Plate,” J. Acoust. Emiss., 14(2), pp. 103–114.
Prosser,  W. H., Hamstad,  M. A., Gary,  J., and O’Gallagher,  A., 1999, “Comparison of Finite Element and Plate Theory Methods for Modeling Acoustic Emission Waveforms,” J. Nondestruct. Eval., 18(3), pp. 83–90.
Vasudevan,  N., and Mal,  A. K., 1985, “Response of an Elastic Plate to Localized Transient Sources,” ASME J. Appl. Mech., 107, pp. 356–362.
MATLAB 6.5, Release 13.
Banerjee,  S., Prosser,  W. H., and Mal,  A. K., 2004, “Analysis of Transient Lamb Waves Generated by Dynamic Surface Sources in Thin Composite Plates,” J. Acoust. Soc. Am., 115, pp. 1905–1911.

Figures

Grahic Jump Location
The locus of the real roots, k2(k1) of g(k1,k2) in the k1–k2 plane
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Schematic of a loaded unidirectional composite plate showing position of the sensors with respect to the fiber direction
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Kernel behavior for a unidirectional graphite/epoxy composite plate of thickness 1 mm for propagation along 45 degh for two cases: (a) at a distance 10 mm from the source at 0.1 MHz and (b) at a distance 50 mm from the source at 1.0 MHz (CPT). (i) Locus of real (k2r) and imaginary roots (k2c) of g(k1,k2) in the k1–k2 plane, (ii) absolute plot of Eq. (3), and (iii) real and imaginary parts of the integrand in Eq. (5).
Grahic Jump Location
Kernel behavior for a unidirectional graphite/epoxy composite plate of thickness 1 mm for propagation along 90 deg at a distance 50 mm from the source at 1 MHz (exact theory). (i), (ii), and (iii) are the same as that of Fig. 3.
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Time history and spectrum of the source
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Time history of vertical surface displacement in a 1 mm thick unidirectional graphite/epoxy composite plate subjected to a point load from exact theory (first column) and FEM (second column), (a) 0 deg propagation, (b) 30 deg propagation, (c) 60 deg propagation, and (d) 90 deg propagation  

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