On the spectrum and stiffness of an elastic body with surface stresses

Holm Altenbach (1) , Victor A. Eremeyev (1) , Leonid P. Lebedev (2)

1 Institut für Mechanik
2 Departamento de Matematicas

A mathematical investigation of the eigenvalue problems for elastic bodies including surface stresses is presented. Weak setup of the problems is based on the Rayleigh variational principle. Certain spectral properties are established for the problems under consideration. In particular, bounds for the eigenfrequencies of an elastic body with surface stresses are presented. These bounds demonstrate increases in both the rigidity of the body and of the eigenfrequencies over those of the body with surface stresses neglected.

Domains: Mechanics [physics.med-ph]

Holm Altenbach, Victor A. Eremeyev, Leonid P. Lebedev. On the spectrum and stiffness of an elastic body with surface stresses. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2011, 91 (9), pp.699-710. ⟨hal-00824109⟩