On asymptotic analysis of spectral problems in elasticity
AUTOR(ES)
Nazarov, S.A., Sokolowski, J.
FONTE
Latin American Journal of Solids and Structures
DATA DE PUBLICAÇÃO
2011
RESUMO
The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectorial setting of the problem, and usage of intrinsic integral characteristics of defects. The asymptotic formulae are developed in a form convenient for application in shape optimization and inverse problems.
