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The Quarterly Journal of Mechanics and Applied Mathematics 1976 29(4):457-466; doi:10.1093/qjmam/29.4.457
© 1976 by Oxford University Press
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WAVE PROPAGATION IN A NONLINEAR LAMINATED MATERIAL: A DERIVATION OF GEOMETRICAL ACOUSTICS

MICHAEL P. MORTELL and BRIAN R. SEYMOUR

( Department of Mathematical Physics, University College Cork, Ireland
Department of Mathematics and Institute of Applied Mathematics and Statistics, University of British Columbia Vancouver, Canada )

The problem of describing the propagation of a wave through a nonlinear elastic laminated composite is considered, under the restriction that the mismatch of successive impedances is small. A theory neglecting all reflections is derived and is shown to limit to the first term in a nonlinear geometrical-acoustics expansion for a nonuniform continuous medium. When the composite has a periodic structure the limiting medium is a nonlinear viscoelastic material.


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