Shock fronts in laminated plates subjected to impact loadings are in vestigated by the ray theory. The kinematic conditions of compatibility and the dynamical conditions on the wave fronts are derived. The propaga tion velocity, the expression for the position of the wave front, and the ray geometry are presented. From the ray geometry, the directions of propa gation along which the wave front decays or grows more rapidly are found. Numerical solutions for cross-ply laminates are discussed.
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References
1.
T.S. Chow, "On the Propagation of Flexural Waves in an Orthotropic Laminated Plate and Its Response to an Impulsive Load," J. Composite Materials , Vol. 5 (1971), p. 306.
2.
F.C. Moon, "Wave Surface Due to Impact on Anisotropic Plates," J. Composite Materials, Vol. 6 ( 1972), p. 62
3.
A.S.D. Wang , P.C. Chou, and J.L. Rose, "Strongly Coupled Stress Waves in Heterogeneous Plates," AIAA Journal, Vol. 10, No. 8 (1972), p. 1088.
4.
J.M. Whitney and N.J. Pagano, "Shear Deformation in Heterogeneous Anisotropic Plates," J. Applied Mechanics, Vol. 37, No. 4 (1970), p. 1031.
5.
C.T. Sun and J.M. Whitney, "On Theories for the Dynamic Response of Laminated Plates," Proceedings AIAA/ASME/SAE 13th Structures, Structural Dynamics, and Materials Conference (1972), AIAA Paper No. 72-398.
6.
J. Hadamard, Lecons sur la Propagation des Ondes et les Equations de l'Hydrodynamique, Paris (1903).
7.
T.Y. Thomas, Plastic Flow and Fracture of Solids, Academic Press (1961).
8.
A.E.H. Love, The Mathematical Theory of Elasticity, Dover, New York (1944), p. 295.
9.
P.R. Garabedian, Partial Differential Equations, John Wiley, New York (1964), p. 27.
10.
H.B. Keller , "Propagation of Stress Discontinuities in Inhomogeneous Elastic Media," SIAM Review, Vol. 6, No. 4 (1964), p. 356.
11.
N.J. Vlaar , "Ray Theory for an Anisotropic Inhomogeneous Elastic Medium," B11. Seism. Soc. Am., Vol. 58, No. 6 (1968), p. 2053.
12.
M. Kline and I.W. Kay, Electromagnetic Theory and Geometrical Optics, John Wiley , New York (1965), p. 155.