An asymptotic model for the free vibrations of a two-layer beam

• We apply the asymptotic development method to study the free vibrations of a generic two-layer beam.
• We investigate the negligibility of axial and rotational inertia.
• We study the negligibility of shear stiffness and of interface stiffness in the normal direction.
• We identify a simplified model for the vibration analysis.
• The reliability of the simplified model is checked analytically.

The free vibrations of a two-layer beam are investigated. The asymptotic development method is applied to assess when axial and rotational inertia, shear deformations and interface normal compliance can be disregarded. In the limit case a simplified model with Euler–Bernoulli kinematics for each layer, and with normal perfect adherence at interface, is obtained. The simplified model has only 2 unknowns (which can be easily reduced to a single unknown), versus the 8 of the original problem, and has only 2 dimensionless parameters, versus the 14 of the original problem, and thus can be handled more easily. Both the limit natural frequencies and their first order corrections are computed; the latter, in particular, permit determination of the sensitivity with respect to the parameters considered.