The transient dynamics of a moving accelerating/decelerating mass traveling on a periodic-array non-homogeneous composite beam

Abstract

Abstract Vibrations of flexible beams with attached moving masses have been the subject of many interests; generally they are based on the assumption that the mass moves along a homogeneous beam. However, in fact, many applications of composite (smart) flexible beams are found in both Civil and Mechanical Engineering. For example, the stationary track of a linear motor system is composed by a row of equally spaced magnetic blocks; a smart beam consists of periodically arranged electroelastic laminas in the beam direction to enhance the resistance of transverse deflection. Obviously, they cannot be treated as homogeneous beams; they should be treated as periodic-array non-homogeneous composite beams. Hence, to develop a mathematical model that can correctly predict the dynamic behavior of such structure is of importance. The aim of this paper then is to present correct formulations to evaluate the transient dynamics of a moving accelerating/decelerating mass traveling on a periodic-array non-homogeneous composite beam. The inhomogeneous beam is assumed to be composed of two different materials. The two different materials are accounted for by spatial variation of the moduli of the two phases. The difficulty of solving composite problem is overcome by treating the composite beam as a single phase inhomogeneous continuum. It becomes a periodic-array in the beam direction. The variation of material properties hence can be expressed by a Fourier series half-range expansion in the axial direction. Based on the assumption that whenever the mass being propelled by a thrust along the path, the thrust on the mass will be along the tangent to the vibrating path, the effects produced by the motion of a mass traveling on a periodic-array composite beam are investigated. The solutions determined by certain physical parameters are also examined.