SMALL OSCILLATIONS OF FINITELY DEFORMED ELASTIC NETWORKS

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 fibre s 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. Mo dal analysis is performed for a sector of a one-parameter family of hy perbolic paraboloids with non-linearly elastic fibres, and the effect of geometric and material non-linearity on the frequency response of t he network is quantified. (C) 1997 Academic Press Limited.