Journal
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
Volume 90, Issue 3, Pages 231-240Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/zamm.200900311
Keywords
Surface stresses; existence theorem; Sobolev's spaces; eigenfrequencies
Categories
Funding
- RFBR [09-01-00459]
- DFG [AL 341/31-1]
- National University of Colombia [1123]
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The mathematical investigation of the initial-boundary and boundary value problems in the linear elasticity considering surface stresses is presented. Weak setup of the problems based on mechanical variational principles is studied. Theorems of uniqueness and existence of the weak solution in energy spaces of static and dynamic problems are formulated and proved. Some properties of the spectrum of the problems under consideration are established. The studies are performed applying the functional analysis techniques. Finally, the Rayleigh principle for eigenfrequencies is constructed. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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