The asymptotic development method is used to study the effects of axial and rotational inertia, of shear deformations and of interface normal compliance in the vibrations of a two-layer beam. Starting from a model with Timoshenko kinematics, a model with Euler-Bernoulli kinematics for each layer, and with normal perfect adherence at interface, is obtained as a limit case. The limit model has only 1 unknown, versus the 8 of the original problem, and has only 2 dimensionless parameters, versus the 14 of the original problem, and thus it is much more easy. The asymptotic approach used to obtain the limit model guarantees on its reliability. Both the limit natural frequencies and their first order corrections are computed; the latter, in particular, permit to determine the sensitivity with respect to the considered parameters.

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