Abstract
The dynamic behavior of multispan uniform continuous beam arbitrarily supported on its edges subjected to various types of moving noninertial loads is studied. Problem is solved by replacing a multispan structure with a single-span beam loaded with a given moving load and redundant forces situated in the positions of the intermediate supports. Redundant forces are obtained by solving Volterra integral equations of the first or the second order (depending on the stiffness of the intermediate supports) which are consistent deformation equations corresponding to each redundant. Solutions for the beam arbitrarily supported on its edges (pinned or fixed) due to a moving concentrated force and moving distributed load are given. The difficulty of solving Volterra integral equations analytically is bypassed by proposing a simple numerical procedure. Numerical examples of two- and three-span beam have been included in order to show the efficiency of the presented method.
Highlights
Many authors have considered the problem of vibrations in structural and mechanical engineering resulting from the moving load, because of both being interesting from the theoretical point of view and having a significant importance for the practice
There are not so many papers focused on the dynamic response problem of a multispan beam due to a moving load [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]
In order to find the solution for multispan continuous beams using a set of the Volterra integral equations, in the first step the dynamic response of a finite, single-span beam subjected to a moving load and stationary point forces is considered
Summary
Many authors have considered the problem of vibrations in structural and mechanical engineering resulting from the moving load, because of both being interesting from the theoretical point of view and having a significant importance for the practice. The solution of the response of a finite, single-span beam subjected to a force moving with a constant velocity has a form of an infinite series and has been presented in many papers. The primary structure (primary beam) is an arbitrarily supported single-span beam For this reason, in order to find the solution for multispan continuous beams using a set of the Volterra integral equations, in the first step the dynamic response of a finite, single-span beam subjected to a moving load and stationary point forces is considered. The correctness of the algorithm has been tested using Finite Difference Method
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