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Mathematics and Mechanics of Solids
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Vibration of a Surface-Coated Elastic Block Subject to Bending

M. Gei

Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, Viale Allegri 13, I-42100 Reggio Emilia, Italy

R. W. Ogden

Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK

In this paper we study the effect of a thin-film elastic surface coating on infinitesimal plane vibrations of a rectangular block of incompressible isotropic elastic material, which is subject to a static pure bending deformation. The equations governing the vibrations superimposed on the bending deformation are derived along with appropriate boundary conditions. The equations are then solved numerically in order to illustrate the dependence of the frequency of vibrations on the aspect ratio and the underlying deformation of the block and on the material parameters of the coating. Comparisons with results for an uncoated block are highlighted and the limiting case of zero frequency (corresponding to bifurcation of the static configuration) is discussed.

Key Words: Nonlinear elasticity • vibrations • coating • bending

Mathematics and Mechanics of Solids, Vol. 7, No. 6, 607-628 (2002)
DOI: 10.1177/108128602029657
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