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SMALL OSCILLATIONS OF FINITELY DEFORMED ELASTIC NETWORKS

Authors
Journal
Journal of Sound and Vibration
0022-460X
Publisher
Elsevier
Publication Date
Volume
202
Issue
5
Identifiers
DOI: 10.1006/jsvi.1996.0795
Disciplines
  • Mathematics

Abstract

Abstract Linearized equations describing small motions superimposed on finitely deformed equilibrium configurations of elastic networks are derived. The theory is based on the so-called membrane model in which the fibres of the network are assumed to be continuously distributed to form a surface. A consistent linearization method is used to obtain equations of motion valid for arbitrary underlying equilibrium deformations. Modal analysis is performed for a sector of a one-parameter family of hyperbolic paraboloids with non-linearly elastic fibres, and the effect of geometric and material non-linearity on the frequency response of the network is quantified.

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