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The Quarterly Journal of Mechanics and Applied Mathematics 1982 35(4):485-507; doi:10.1093/qjmam/35.4.485
© 1982 by Oxford University Press
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BENDING WAVES IN STRONGLY ANISOTROPIC ELASTIC PLATES

W. A. GREEN

( Department of Theoretical Mechanics, University of Nottingham )

Dispersion relations, giving phase velocity as a function of wavelength, are obtained for flexural waves (Lamb waves) in a plate of transversely isotropic material with the axis of transverse isotropy lying in the plane of the plate. Solutions are obtained for the idealized material which is inextensible in the direction of the axis of transverse isotropy and these are compared with solutions for the almost inextensible material. It is shown that the dispersion relation for the idealized material gives a good approximation to that of the almost inextensible material at intermediate and short wavelengths but not in the long-wavelength region. Numerical results show the existence of a boundary layer of high tensile and compressive stresses at the upper and lower surfaces of the plate of almost inextensible material at the short and intermediate wavelengths, with an associated rapid variation in shear stress. For the long-wavelength motion, the stress distribution is the linear variation through the plate which is normally associated with pure bending.


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