Vibration analyses of a portal frame under the action of a moving distributed mass using moving mass element

Four kinds of moving mass elements, 1st-node, 2nd-node, full and short-range mass elements, are presented, where the 1st-node (or 2nd-node) mass element refers to that with mass distributed from the first node (or second node) to the arbitrary position of a two-node beam element, the full mass element is the special case of the 1st-node (or 2nd-node) mass element with mass distributed over the full length of the beam element, while the short-range mass element is the case with its location arbitrary on a beam element. If the total range of a distributed mass is denoted by R and the length of each beam element is denoted by , then, for the case of R , one may model the distributed mass on the beam using the combination of the 1st-node, 2nd-node and full mass elements, while for the case of R< , one may model the distributed mass using the short-range mass element. It has been found that the effects of the vertical (¯y ) and horizontal (¯x) inertia forces, Coriolis force and centrifugal force induced by the moving distributed mass can be easily taken into the formulations by means of the last concept. To illustrate the application of the presented theory, the dynamic analysis of a pinned–pinned beam and that of a portal frame under the action of a moving uniformly distributed mass are performed by means of the finite element method and the Newmark integration method. Numerical results show that some pertinent factors, such as Coriolis force, centrifugal force, acceleration, velocity and total range of the moving distributed mass, have significant influences on the vertical (¯y ) and horizontal (¯x ) response of a structure