Moderately large vibrations of flexibly bonded layered beams with initial imperfections

Abstract

In this paper, a beam theory is presented that allows to compute the moderately large dynamic response of slightly curved linear elastic layered beams with interlayer slip. The considered structural members are immovably supported, which leads to non-negligible membrane stresses at moderately large bending vibrations, and consequently to a geometrically nonlinear response. Based on a layerwise application of the Euler–Bernoulli theory, the boundary value problem is formulated for an arbitrary number of layers. A specification is then made for two- and three-layer beams. Several examples show the effect of an imperfect beam axis on the nonlinear dynamic response. A comparison of selected results with those of a much more expensive finite element analysis based on a plane stress state demonstrates the accuracy of the beam theory proposed.