Vibration of composite beams with deformable shear connection: Mathematical modelling and numerical solution using general-purpose software for two-point boundary value problems

Abstract In this paper, we develop from first principles a linear one-dimensional mathematical model for the dynamic response of planar composite beams with deformable shear connection, in which the inertias associated with the axial motion of the components and with the bending rotations of their cross-sections are consistently taken into account. To the best of our knowledge, the paper by Auclair et al. [J. Sound Vib. 366 (2016) 230–247] is the only work which heretofore considered these two effects. However, we point out and correct a flaw in the derivations of these authors. To solve the eigenproblem defining the natural vibration frequencies of the composite beam and the corresponding vibration modes, we advocate an untried approach – the eigenproblem is converted into a “standard” inhomogeneous boundary value problem, which can be solved using freely available state-of-the-art mathematical software. For benchmarking purposes, the formulation of a conventional displacement-based conforming finite element is also briefly addressed. The effect of rotational and axial inertias on the natural vibration frequencies is found to be marginal and considerably less pronounced than the predictions of Auclair and coworkers. In disagreement with the findings of these authors, it appears legitimate to ignore the above-mentioned effect in a full dynamic analysis of composite beams, at least within the practical range of span-to-depth ratios.