Vibration response of Euler-Bernoulli-damped beam with appendages subjected to a moving mass

This paper addresses the problem of a viscoelastic Euler-Bernoulli beam under the influence of a constant velocity moving mass and different types of appendages. Four types of boundary conditions are considered: pinned-pinned, fixed-pinned, fixed-free (or cantilever), and fixed-fixed. Appendages considered include lumped masses, dampers, and springs. The modal decomposition method is employed to derive the equation of motion of the beam, for which an analytical closed-form expression of the dynamic vibration response is generated. The proposed method enables the study of the effect of a single appendage or a combination of the three types of appendages on the non-dimensional dynamic response of the beam. Numerical examples are presented to illustrate the effects of these appendages and compare them to the reference cases of a beam with no appendages. The results demonstrate the importance of considering these parameters in the design of structures. The proposed method is compared to other techniques in the literature and found to be advantageous due to its direct approach. The method also offers a versatile tool for investigating various configurations, aiding in engineering design and structural analysis for which establishing a precise prediction of beam vibrations is crucial.