Some applications of the WKB method to the wrinkling of biannular plates in tension
 Ciprian D. Coman
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An application of WKB methods is proposed here for a stretched annular thin plate with piecewiseconstant mechanical properties (also known as a biannular plate). Unlike the classical scenario involving only a simple annular such plate, in certain cases the neutral stability curve fails to be convex and the critical eigenmodes behave rather differently as the plate becomes progressively thinner (equivalent to \({\mu \to \infty}\) in our notations). On one side of this curve, the corresponding eigenmodes are localised near the inner rim of the annulus, while in the remaining part these functions are concentrated along the interface separating the two annular subregions. By using the asymptotic reduction technique proposed by Coman and Haughton in (Acta Mech 185:179–200, 2006), the original fourthorder threepoint boundaryvalue problem is formally reduced to a pair of secondorder differential equations coupled through a set of matching conditions at the interface. It is shown that for \({\mu \gg 1}\) the critical eigenvalues for both cases mentioned above can be approximated by solving a couple of simple transcendental equations and that the results predicted compare well with the direct numerical simulations of the original problem.
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 Title
 Some applications of the WKB method to the wrinkling of biannular plates in tension
 Journal

Acta Mechanica
Volume 224, Issue 2 , pp 399423
 Cover Date
 20130201
 DOI
 10.1007/s0070701207616
 Print ISSN
 00015970
 Online ISSN
 16196937
 Publisher
 Springer Vienna
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 Authors

 Ciprian D. Coman ^{(1)}
 Author Affiliations

 1. Schlumberger Gould Research, High Cross, Madingley Road, Cambridge, CB3 0EL, England