Free and forced small flexural vibrations of slightly curved slender composite beams with interlayer slip. (November 2022) - Adam, Christoph; Ladurner, Dominik; Furtmüller, Thomas
Abstract: This paper presents a beam theory for analyzing the dynamic bending response of slender slightly curved composite beams whose layers are flexibly connected and therefore subject to interlayer slip. The equations of motion and boundary conditions are derived using Hamilton's principle, assuming separately for each layer the applicability of Euler–Bernoulli theory and a linear elastic relationship between the interlayer slip and the shear traction. For the problem of a three-layer slightly curved single-span beam with symmetric layer arrangement and soft-hinged bearings, analytical expressions for the natural frequencies and the eigenfunctions are derived. For the arbitrarily supported two-layer beam, on the other hand, a numerical solution scheme of the combined initial boundary value problem is presented. Several examples show how important it is to consider even very small deviations from the straight beam axis in the prediction of the dynamic response for slender beams with interlayer slip, in particular when all supports are immovable. The comparison of the beam solutions with the results of much more expensive FE analyses based on plane stress elasticity proves the accuracy of the presented theory. Highlights: First beam theory for dynamic analysis of slightly curved beam with interlayer slip. Analytical solution for three layer-beams with symmetrically arranged layers. Numerical solution procedure for more general members with interlayer slip. The grave effect of the initial curvature on the dynamic response is shown. Accuracy of the theory is shown by comparison with FE plane stress solutions.