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Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates. (English) Zbl 0727.73030
The author is concerned with a mathematical analysis of von Kármán’s equations for the stability of a viscoelatic circular clamped plate. The viscoelastic plate of constant thickness is under a uniform compressive load which is applied on its midplane along its edge and depends on a real parameter, with zero initial conditions. The structural buckling pattern of von Kármán’s equations for the viscoelastic plate is analyzed from the point of view of nonlinear functional analysis. Various properties of solutions for the buckling of viscoelastic plate are studied in detail. Also, the operator and integro-operator formulations are derived for the buckling and post-buckling behavior of the viscoelastic circular plate. The paper exhibits some qualitatively different features of the viscoelastic plate as compared to elastic ones. The results presented are purely theoretical in nature and need to be applied to some critical modes of the viscoelastic plate, as stated.

74K20 Plates
74G60 Bifurcation and buckling
35D99 Generalized solutions to partial differential equations
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