Abstract
Shear deformation and rotary inertia are included in plate theory to determine the dispersion curves for flexural waves propagating in laminated composite plates. The results of a unidirectional laminate are compared with the elasticity solutions for flexural waves traveling in transversely isotropic plates to determine the shear correction factors in the low frequency, long wavelength range. The values of the shear correction factors for the unidirectional composite laminate are in good agreement with the theoretical values calculated from static cylindrical bending. An acousto-ultrasonic technique using narrowband excitation frequencies is used to obtain experimental data for flexural waves. By measuring the phase velocities for different excitation frequencies, dispersion curves are generated. There is excellent agreement between the experimentally determined values and the theoretical results for aluminum and unidirectional composite plates. For symmetric cross-ply and quasi-isotropic laminates, the data definitely have the characteristic of a dispersion curve for flexural waves, although the agreement between analytic and experimental results is not quite as good. The results of the present work indicate that the inclusion of shear deformation and rotary inertia in plate theory improves the prediction of dispersion curves for flexural waves propagating in composite laminates and suggest that the acousto-ultrasonic technique can be used to characterize composite plates with and without damage since each material and stacking sequence gives distinct dispersion curves.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Lamb, On Waves in an Elastic Plate, Proc of the Royal Soc of London, Series A, 93:114 (1917).
R. D. Mindlin, Waves and Vibrations in Isotropic, Elastic Plates, in: “Structural Mechanics,” J. N. Goodier and N. J. Hoff, eds., Pergamon Press, New York (1960 )
M. Redwood, “Mechanical Waveguides,” Pergamon Press, New York (1960)
T. R. Meeker and A. H. Meitzler, Guided Wave Propagation in Elongated Cylinders and Plates, in: “Physical Acoustics: Principles and Methods,” W. P. Mason, ed., Academic Press, New York (1964).
I. A. Viktorov, “Rayleigh and Lamb Waves,” Plenum Press, New York (1967).
H. Ekstein, High Frequency Vibrations of Thin Crystal Plates, Phys Y Rev. 68:11 (1945) .
W. R. Rose, S. I. Rokhlin, and L. Adler, Evaluation of Anisotropic Properties of Graphite/Epoxy Composite Plates Using Lamb Waves, in: “Review of Progress in Quantitative NDE, Vol. 6B,” D. O. Thompson and D. E. Chimenti, eds., Plenum Press, New York (1987) .
D. E. Chimenti and A. H. Nayfeh, Leaky Lamb Waves in Fibrous Composite Laminates, J of Appl Phys. 58:4531 (1985) .
W. T. Yost and J. H. Cantrell, Surface Generation and Detection of Coupled Fiber-Matrix Mode Acoustic Wave Propagation in FiberReinforced Composites, in: “Review of Progress in Quantitative NDE, Vol 5B,” D. O. Thompson and D. E. Chimenti, eds., Plenum Press, New York (1986).
R. C. Stiffler and E. G. Henneke II, “The Application of Low Frequency Acoustic Waves for Determining the Extensional and Flexural Stiffnesses in Composite Plates, Interim Report to General Electric Co., Contract No. 14-G-45–480,” Virginia Tech, Blacksburg (1985).
J. C. Duke Jr., E. G. Henneke, II, and W. W. Stinchcomb, “Ultrasonic Stress Wave Characterization of Composite Materials, NASA CR-3976,” NASA, Cleveland (1986) .
R. C. Stiffler, “Wave Propagation in Composite Plates,” Ph.D. Dissertation, College of Engineering, Virginia Polytechnic Institute and State University, Blacksburg. (1986).
P. C. Yang, C. H. Norris, and Y. Staysky, Elastic Wave Propagation in Heterogeneous Plates, Intl J of Solids and Struc. 2:665 (1966) .
R. D. Mindlin, Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates, J of Appl Mech. 18:31 (1951) .
C. T. Sun and T. M. Tan, Wave Propagation in a Graphite/Epoxy Laminate, J of the Astro Sc. 32:269 (1984).
W. A. Green, Bending Waves in Strongly Anisotropic Elastic Plates, Quarterly J of Mech and Appl Math. 35:485 (1982) .
J. M. Liu, The Frequency Dependence of Ultrasonic Wave Propagation in Metal-Matrix Composite Plates, in: “Proceedings of the 15th Symposium on NDE,” D. W. Moore and G. A. Matzkanin, eds., Southwest Research Institute, San Antonio (1985).
T. S. Chow, On the Propagation of Flexural Waves in an Orthotropic Laminated Plate and Its Response to an Impulsive Load, J of Comp Matls. 5:306 (1971).
J. M. Whitney, Shear Correction Factors for Orthotropic Laminates Under Static Load, J of Appl Mech. 40:302 (1973).
E. Reissner, The Effect of Transverse Shear Deformation on the Bending of Elastic Plates, J of Appl Mech. 12:69 (1945).
A. K. Noor, Stability of Multilayered Composite Plates, Fibre Sc and Tech. 8:81 (1975).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer Science+Business Media New York
About this chapter
Cite this chapter
Tang, B., Henneke, E.G., Stiffler, R.C. (1988). Low Frequency Flexural Wave Propagation in Laminated Composite Plates. In: Duke, J.C. (eds) Acousto-Ultrasonics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1965-9_4
Download citation
DOI: https://doi.org/10.1007/978-1-4757-1965-9_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-1967-3
Online ISBN: 978-1-4757-1965-9
eBook Packages: Springer Book Archive