Effect of friction on transverse vibration of string under moving load

Many engineering applications involve exerting moving harmonic load on a string like structure. Usually the interface between these structures and the moving load has some friction. A common example is a pantograph catenary system, which is used in locomotives for power collection. The aim of this paper is to develop a mathematical model of a simplified system consisting of infinitely long axially tensioned continuum and a moving harmonic load with friction acting at the interface. Equation of motion has been derived by resolving forces at that point. Subsequently the basic characteristics of the system are obtained by solving the model numerically. It is observed that the effect of friction obtained is negligibly low higher value of axial tension, but can significantly increase the string response at a particular range of coefficient of friction value when the axial tension is low.

VIBRATION OF 2D-FGSW TIMOSHENKO BEAMS UNDER A MOVING HARMONIC LOAD

Vibration of two-directional functionally graded sandwich (2D-FGSW) Timoshenko beams under a moving harmonic load is investigated. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with the material properties continuously varying in both the thickness and length directions by power functions. A finite element formulation is derived and employed to compute the vibration characteristics of the beams. The obtained numerical result reveals that the material inhomogeneity and the layer thickness ratio play an important role on the natural frequencies and dynamic response of the beams. A parametric study is carried out to highlight the effects of the power-law indexes, the moving load speed and excitation frequency on the vibration characteristics of the beams. The influence of the beam aspect ratio on the vibration of the beams is also examined and discussed.

Moving Element Method for Dynamic Analyses of Functionally Graded Plates Resting on Pasternak Foundation Subjected to Moving Harmonic Load

This paper presents the moving element method (MEM) for dynamic analyses of functionally graded (FG) plates resting on Pasternak foundation under moving harmonic load. The Mindlin plate theory is used to model the FG plates. Macroscopic material properties of FG plates are assumed to continuously vary across the thickness direction by a simple power-law distribution. The governing equation of the FG plate is formulated in a coordinate system which moves along with the applied load. In addition, the method simply treats the moving load as “stationary” at the discretized node of plate to completely eliminate the update procedure of force vector due to the change of contact point with elements. To verify the accuracy of the computational paradigm, static and free vibration analyses of FG plates are examined first. Dynamic analyses of FG plates subjected to a moving harmonic load are then conducted to investigate the effects of various parameters such as volume fraction exponent, Young’ modulus, load velocity, foundation damping coefficient and load acceleration/deceleration on dynamic responses of the plate.