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Mathematics and Mechanics of Solids
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Finite-Amplitude, Shockless, Resonant Vibrations of an Inhomogeneous Elastic Panel

Michael P. Mortell

Department of Applied Mathematics, University College, Cork, Ireland

Brian R. Seymour

Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada

An inhomogeneous, nonlinear elastic panel, fixed at one end, is subject to a resonant harmonic forcing at the other. The vibrations in an equivalent homogeneous panel would contain shocks. We exhibit a class of finite inhomogeneities that produces a panel response that is harmonic but does not contain shocks. The finite-strength inhomogeneity is capable of inhibiting the nonlinear distortion sufficiently to prevent shocks from forming. This is not the case for a "slow" inhomogeneity that can be described using a geometrical acoustics approximation.

Key Words: resonant nonlinear oscillations • finite inhomogeneity • shockless motion

Mathematics and Mechanics of Solids, Vol. 10, No. 4, 427-440 (2005)
DOI: 10.1177/1081286505036411
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