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Harmonic vibration of cusped plates in the N-th approximation of Vekua’s hierarchical models
Arch. Mech. 65 (5), 345-365, 2013
Keywords: cusped plates; cusped prismatic shells; degenerate elliptic systems; weighted spaces; Hardy’s inequality; Korn’s weighted inequality
Abstract
In this paper elastic cusped symmetric prismatic shells (i.e., plates of variable thickness with cusped edges) in the N-th approximation of Vekua’s hierarchical models are considered. The well-posedness of the boundary value problems (BVPs) under the reasonable boundary conditions at the cusped edge and given displacements at the non-cusped edge is studied in the case of harmonic vibration. The classical and weak setting of the BVPs in the case of the N-th approximation of hierarchical models is considered. Appropriate weighted functional spaces are introduced. Uniqueness and existence results for the variational problem are proved. The structure of the constructed weighted space is described and its connection with weighted Sobolev spaces is established.