Dynamic Response of a Double Beam System with Nonlinear Variable-Stiffness Viscoelastic Layer under a Moving Load

This study investigates the dynamic response of a simply supported double beam system interconnected through a viscoelastic nonlinear variable stiffness layer with a Winkler support beneath the lower beam and traversed by a moving force. The governing equations were formulated to account for the nonlinear variable stiffness, viscoelastic coupling, foundation stiffness, and moving force velocity. The Fourier sine integral transform was employed to simplify the spatial dependence of the governing equations, while differential transform method are applied to obtain an analytical representation of the dynamic response. Parametric analyses are conducted to examine the effects of moving force velocity, viscoelasticity, nonlinear variable stiffness, interlayer stiffness, and Winkler foundation stiffness on the responses of the upper and lower beams. The results show that increasing the moving force velocity increases the response amplitudes of the beams due to enhanced dynamic excitation and load transmission through the interconnecting layer. Increasing the viscoelastic parameter reduces the responses of both beams as a result of increased energy dissipation. Higher nonlinear variable stiffness and interlayer stiffness drive the upper beam response towards rigid coupling but increase the lower beam response through enhanced load transfer. Increasing the Winkler foundation stiffness promotes rigid coupling in the upper beam and brings the lower beam response closer to the rigid coupling condition. The findings provide insight into the influence of coupling and foundation parameters on the vibration behaviour of nonlinear double beam systems subjected to moving forces.