The method used in the analysis is Newtonian. The mechanics of the interface between the moving mass and the beam is determined by modeling the mass as a rigid body that is rolling on the eccentric axis when the mass is set on motion; moment of the moving mass acting on the beam along the eccentric path is taken into account. Based on Euler-Bernoulli beam theory and inextensibility constraint, the mechanics, including effects due to friction and convective accelerations, of the interface between the mass and the beam is obtained. By employing Galerkin鈥檚 procedure to eliminate spatial dependence, the problem reduces to a multi-degrees-of-freedom dynamical system with time dependent coefficients.
Result of present study indicates that the eccentricity of eccentric path plays an important role to the dynamics of a beam-mass system. If the shape of the eccentric path is concave upward, the amplitude of eccentricity amplifies not only the positive amplitude of the trajectory of mass but also the negative displacement of the beam even if the amplitude of eccentricity is tiny. However, if the shape of the eccentric path is convex upward, the amplitude of eccentricity attenuated the displacement of the beam. In addition, it is generally true that as the mass moves from the left end, the occurrence of negative displacement exists when the mass is subjected by a reverse force and approaches to the right terminal.