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TECHNICAL PAPERS

Elastic Wave Propagation in Circumferential Direction in Anisotropic Cylindrical Curved Plates

[+] Author and Article Information
S. Towfighi, T. Kundu, M. Ehsani

Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, AZ 85721

J. Appl. Mech 69(3), 283-291 (May 03, 2002) (9 pages) doi:10.1115/1.1464872 History: Received April 05, 2001; Revised November 01, 2001; Online May 03, 2002
Copyright © 2002 by ASME
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References

Viktorov,  I. A., 1958, “Rayleigh-Type Waves on a Cylindrical Surface,” Sov. Phys. Acoust., 4, pp. 131–136.
Qu. J., Berthelot, Y., and Li, Z., 1996, “Dispersion of Guided Circumferential Waves in a Circular Annulus,” Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti, eds., Plenum, New York, 15 , pp. 169–176.
Grace,  O. D., and Goodman,  R. R., 1966, “Circumferential Waves on Solid Cyliners,” J. Acoust. Soc. Am., 39, pp. 173–174.
Brekhovskikh,  L. M., 1968, “Surface Waves Confined to the Curvature of the Boundary in Solid,” Sov. Phys. Acoust., 13, pp. 462–472.
Cerv,  J., 1988, “Dispersion of Elastic Waves and Rayleigh-Type Waves in a Thin Disc,” Acta Tech. CSAV, 89, pp. 89–99.
Liu,  G., and Qu,  J., 1998, “Guided Circumferential Waves in a Circular Annulus,” ASME J. Appl. Mech., 65, pp. 424–430.
Liu,  G., and Qu,  J., 1998, “Transient Wave Propagation in a Circular Annulus Subjected to Impulse Excitation on Its Outer Surface,” J. Acoust. Soc. Am., 103, pp. 1210–1220.
Valle,  C., Qu,  J., and Jacobs,  L. J., 1999, “Guided Circumferential Waves in Layered Cylinders,” Int. J. Eng. Sci., 37, pp. 1369–1387.
Nayfeh, A. H., 1995, Wave Propagation in Layered Anisotropic Media With Application to Composites, Elsevier, Amsterdam.
Armenakas,  A. E., and Reitz,  E. S., 1973, “Propagation of Harmonic Waves in Orthotropic, Circular Cylindrical Shell,” ASME J. Appl. Mech., 40, pp. 168–174.
Mal, A. K., and Singh, S. J., 1991, Deformation of Elastic Solids, Prentice-Hall, Englewood Cliffs, NJ, p. 313.
Karim,  M. R., Mal,  A. K., and Bar-Cohen,  Y., 1990, “Inversion of Leaky Lamb Wave Data by Simplex Algorithm,” J. Acoust. Soc. Am., 88, pp. 482–491.
Rose, J. L., 1999, Ultrasonic Waves in Solid Media, Cambridge University Press, Cambridge, U.K., pp. 264–271.
Towfighi, S., 2001, “Elastic Wave Propagation in Circumferential Direction in Anisotropic Pipes,” Ph.D. dissertation, The University of Arizona, Tucson, AZ.

Figures

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Waves propagating from section T to R in a curved plate. Wave speed is proportional to radius of curvature.
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Stress and displacement components in cylindrical coordinate system
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Dispersion curves for isotropic flat plate (11). Plate thickness=1 mm.
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Dispersion curves generated by the proposed method. Plate thickness=1 mm. Pipe outside radius=1.0 m.
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Tangential direction of the fibers maintains the symmetry. Coordinate systems for flat-plate and pipe analyses are also shown.
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Dispersion curves of a unidirectional composite plate for waves propagating in fiber direction (x-axis direction, 0 deg). Material properties are given in Eq. (12), ρ=1580 kg/m3 (3).
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Dispersion curves for a large-diameter pipe made of an anisotropic material. Material properties are given in Eq. (12). Pipe wall thickness=1 mm. Pipe outer radius=1000 mm,m=30.
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Dispersion curves for the anisotropic pipe with m=20. Pipe dimensions and material properties are same as in Fig. 7, only m is different.
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Dispersion curves of unidirectional composite plate for waves propagating perpendicular to the fiber direction (x-axis direction, 90 deg). Material properties are given in Eq. (13). Plate thickness=1 mm,ρ=1580 kg/m3 (3).
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Computed dispersion curves for an anisotropic large diameter pipe, when fiber and wave propagation directions are perpendicular to each other. Material properties are given in Eq. (13). Pipe wall thickness=1 mm. Pipe outer radius=1000 mm.
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(a) Dispersion curves for symmetric modes for a unidirectional composite plate for waves propagating in 45 deg to the fiber direction. Plate thickness=1 mm and ρ=1580 kg/m3 (3). (b) Dispersion curves for antisymmetric modes for a unidirectional composite plate for waves propagating in 45 deg to the fiber direction. Plate thickness=1 mm and ρ=1580 kg/m3 (3).
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Dispersion curves for a large diameter pipe made of an anisotropic material. Material properties are given in Eq. (14). Pipe wall thickness=1 mm. Pipe outer radius=1000 mm,m=25.
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Dispersion curves for aluminum pipe obtained by the proposed method. η (ratio of inner to outer radius)=0.1.
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Dispersion curves for aluminum pipe obtained by Qu et al. 2. Material properties are not known.
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Dispersion curves for circumferential direction wave propagation in fiber-reinforced cylindrical composite plates when fibers are oriented in the circumferential direction, outer radius of the pipe is (a) 1000 mm, (b) 10 mm, (c) 5 mm, and (d) 2.5 mm. Pipe wall thickness and material properties are same as those in Fig. 7.
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Dispersion curves for circumferential direction wave propagation in fiber-reinforced composite cylindrical plates when fibers are oriented in the axial direction, outer radius of the pipe is (a) 1000 mm, (b) 10 mm, (c) 5 mm, and (d) 2.5 mm. Pipe wall thickness and material properties are same as those in Fig. 9.
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Dispersion curves for the curved plate when the fibers are oriented in the 45 deg direction. Material properties are given in Eq. (14). Outer radius is 5 mm. Thickness=1 mm. Right figure is for m=25, and the left figure is for m=35. Frequency range for the left figure is 0 to 1 MHz and for the right figure it is 0 to 6 MHz.

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