Dynamic response of continuous beams with discrete viscoelastic supports under sinusoidal loading

Analysis of vibrations of continuous beams with discrete viscoelastic supports has been established through theoretical modeling and a finite element analysis. The theoretical model is based on the Euler-Bernoulli theory, and the Ritz approach was employed to obtain numerical results from which the attenuation of the beam’s vibration was obtained. In parallel, a finite element analysis was carried out in ABAQUS using 3D beam elements. It is shown that the results of theoretical calculation agree well with those of the finite element analysis. Both models were applied to explore geometric and design variations, and then to a full model of a bridge expansion unit as an application example. The vibration of the beams in the design, the influence of the stiffness and the viscous damping coefficient of the supports were discussed, demonstrating the models’ usefulness in helping with design optimization.