Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Unsymmetric deformation of the circular membrane


Author: R. W. Dickey
Journal: Quart. Appl. Math. 44 (1986), 81-90
MSC: Primary 73K15
DOI: https://doi.org/10.1090/qam/840445
MathSciNet review: 840445
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Abstract: If the Föppl equations for the deformation of a plane circular membrane under normal pressure are linearized about the radially symmetric solution, it is shown that the resulting linear theory has infinitely many nontrivial angle-dependent solutions. If the prescribed normal pressure and the prescribed (angle-independent) boundary stress are allowed to approach zero in the appropriate way, these nontrivial solutions are retained. Thus the linear theory indicates that, in addition to the solution with radial symmetry, there are infinitely many angle-dependent solutions for arbitrarily small values of the prescribed pressure and prescribed boundary stress.


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DOI: https://doi.org/10.1090/qam/840445
Article copyright: © Copyright 1986 American Mathematical Society


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