Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/1581
Title: Eigenvalue of a semi-infinite elastic strip
Authors: Zernov, V
Pichugin, AV
Kaplunov, JD
Keywords: edge resonance;vibration;semi-infinite strip
Issue Date: 2006
Publisher: Royal Society Publishing
Citation: Proceedings of the Royal Society of London, Series A, 462(2068), pp. 1255–1270 (2006).
Abstract: A semi-infinite elastic strip, subjected to traction free boundary conditions, is studied in the context of in-plane stationary vibrations. By using normal (Rayleigh–Lamb) mode expansion the problem of existence of the strip eigenmode is reformulated in terms of the linear dependence within infinite system of normal modes. The concept of Gram's determinant is used to introduce a generalized criterion of linear dependence, which is valid for infinite systems of modes and complex frequencies. Using this criterion, it is demonstrated numerically that in addition to the edge resonance for the Poisson ratio ν=0, there exists another value of ν≈0.22475 associated with an undamped resonance. This resonance is best explained physically by the orthogonality between the edge mode and the first Lamé mode. A semi-analytical proof for the existence of the edge resonance is then presented for both described cases with the help of the augmented scattering matrix formalism.
URI: http://bura.brunel.ac.uk/handle/2438/1581
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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