Parametric Analyses of Multispan Viscoelastic Shear Deformable Beams Under Excitation of a Moving Mass

This paper presents a numerical parametric study on design parameters of multispan viscoelastic shear deformable beams subjected to a moving mass via generalized moving least squares method (GMLSM). For utilizing Lagrange’s equations, the unknown parameters of the problem are stated in terms of GMLSM shape functions and the generalized Newmark-$β$ scheme is applied for solving the discrete equations of motion in time domain. The effects of moving mass weight and velocity, material relaxation rate, slenderness, and span number of the beam on the design parameters and possibility of mass separation from the base beam are scrutinized in some detail. The results reveal that for low values of beam slenderness, the Euler–Bernoulli beam theory or even Timoshenko beam theory could not predict the real dynamic behavior of the multispan viscoelastic beam properly. Moreover, higher beam span number would result in higher inertial effects as well as design parameters values. Also, more distinction has been observed between the predicted values of design parameters regarding the shear deformable beams and those of Euler–Bernoulli beams, specifically for high levels of moving mass velocity and low values of material relaxation rate. Furthermore, the possibility of mass separation from the base beam moves to a greater extent as the beam span number increases and the relaxation rate of the beam material decreases, regardless of the assumed beam theory.