Closed-form solutions for forced vibrations of a cracked double-beam system interconnected by a viscoelastic layer resting on Winkler–Pasternak​ elastic foundation

A double-beam system, which consists of two parallel beams connected by a viscoelastic layer, has found broad application in practical engineering such as continuous dynamic absorbers and floating-slab tracks. During the structural service period, the crack is one of the most common defects, which poses a great threat to its normal operation and safety. As a first endeavor, this paper strives to obtain the closed-form solutions for steady-state forced vibrations of a cracked double-beam system resting on the Winkler–Pasternak elastic foundation subjected to harmonic loads. The mechanical properties of cracked cross-sections are characterized by the local stiffness model. Due to the existence of cracks, the cracked double-beam system is artificially divided into several intact segments, where fundamental dynamic responses of each segment are achieved by the Green’s functions method. Subsequently, the transfer matrix method is employed to obtain the steady-state responses of the whole cracked system via the compatibility conditions of cracked cross-sections and boundary conditions. Numerical calculations are performed to check the validity of the present solutions and to discuss the influences of some important parameters, such as crack geometries and connecting layer stiffness, on dynamic behaviors of cracked double-beam systems. Significant effects of the crack depth and location are revealed on the natural frequency and dynamic responses of the system. It is highlighted that based on the bending moment diagram of the mode shape of the intact double-beam system, the effect of the crack location on dynamic behaviors of its cracked system can be effectively predicted.