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a dynamic green function formulation for the response of a beam structure to a moving mass.pdf

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a dynamic green function formulation for the response of a beam structure to a moving mass

Journal of Sound and Vibration (1998) 210(3), 295–306 A DYNAMIC GREEN FUNCTION FORMULATION FOR THE RESPONSE OF A BEAM STRUCTURE TO A MOVING MASS M. A. F??? ??? Z. A?????????? Mechanical Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia (Received 12 March 1997, and in final form 20 June 1997) A dynamic Green function approach is used to determine the response of a simply supported Bernoulli–Euler beam of finite length subject to a moving mass traversing its span. The proposed method produces a simple matrix expression for the deflection of the beam. The efficiency and simplicity of the method is demonstrated by several numerical examples. The effect of various parameters on the dynamic response is investigated. 7 1998 Academic Press Limited 1. INTRODUCTION The moving load problem is a fundamental problem in structural dynamics. The importance of this problem is manifested in numerous applications in the field of transportation. Bridges, guideways, overhead cranes, cableways, rails, roadways, runways, tunnels and pipelines are example of structural elements to be designed to support moving masses. Also, in connection with the design of machining processes, many members can be modelled as beams acted upon by moving loads. The challenge of these designs has attracted the attention of many investigators since 1897, when the Chester Rail Bridge collapsed in England [1]. Various kinds of problems associated with moving loads have been presented in the excellent monograph by Fry?ba [2]. More recent developments and results can be found in state-of-the-art reviews [3–8]. The first dynamic analyses of structures under moving loads involved a simply supported beam in two limiting cases. In the first case, the effects of the load inertia were neglected in the analysis, and the problem is commonly called a moving force approximation. The methods of solution were generally within the framework of modal expansion and lin