Exact dynamic analysis of composite beams with partial interaction

The partial differential equations and general solutions for the deflection and internal actions and the pertaining consistent boundary conditions are presented for composite Euler-Bernoulli members with interlayer slip subjected to general dynamic loading. Both free and forced vibrations are treated. The solutions are shown to be unique and complete under certain conditions, and valid for all so-called restricted admissible boundary conditions. Specifically, the exact eigenmode length coefficients are derived for the four Euler BC. They differ from those valid for ordinary, fully composite (solid) beams, except for the pinned-pinned case. The maximum deviation for beams with the other three Euler BC is shown to be less than 2-6% with respect to the eigenmode length coefficient and 3-10% with respect to the eigenfrequency, respectively, depending on the two non-dimensional parameters, composite action or shear connector stiffness and relative bending stiffness parameters. However, these deviations occur in a rather narrow range of the determining parameters, so for most practical cases the eigenmode length coefficients given for solid (fully composite) beams can approximately be used also for partially composite beams. The procedures of analysing beam vibrations are applied to a specific case. These solutions illustrate the effect of interlayer connection on the peak velocity of the beam vibrations. The proposed analytical theory is verified by tests and finite element calculations.