Abstract <p>We solve a problem of forced flexural vibrations of a strip-like rod with two cantilevers and a finite-length bonded region on one of the outer surfaces. The classical Kirchhoff–Love model is used to describe the cantilever deformation processes, while the deformation of the bonded region is investigated using a refined Timoshenko shear model with account for transverse normal strain, modified by allowing for prescribed motions of the supporting element. We formulate kinematic conditions for coupling the bonded region with the cantilevers. These conditions are applied to derive equations of motion and boundary conditions, as well as force continuity conditions at the junctions of the rod regions, on the basis of the Hamilton–Ostrogradsky principle. An exact analytical solution is constructed for the problem of harmonic forced vibrations under the action of a harmonic transverse force at the end of one of the rod cantilevers. Numerical experiments are performed to study the forced flexural vibrations of a D16AT duralumin rod. Evidently, the vibrations of the unloaded rod cantilever are mainly caused by the prescribed motions of the supporting element.</p>