Dynamic response of slightly curved and supported beams under moving loads

Thesis Type: Doctorate

Institution Of The Thesis: Bursa Uludağ University, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2009

Thesis Language: Turkish

Student: Murat Reis

Supervisor: YAŞAR PALA


This study is devoted to the investigation of dynamic analysis of the beams under moving load. The analysis is based on Euler-Bernoulli beam theory. First Eigen functions of the various types of beams have been obtained than the dynamic response of supported, curved and cracked beams under moving loads have been investigated. Each vertical support is modeled as a linear spring and a linear damper. The present method utilizes the concept of distributed moving load, spring force and damping force, and avoids the use of matching conditions. Expressing these forces in terms of the unknown function of the problem highly simplifies obtaining an exact solution. An important property of Dirac delta distribution function is utilized in order to reach the exact solution. A solution method similar to the method of successive approximation has been used. This study is devoted to the investigation of the effects of inertial, centripetal and Coriolis forces on the dynamic response of a simply supported beam with a single crack under moving mass load. As in the case of beams without a crack, it is shown that these forces must be considered in the analysis. The inertial, centripetal and Coriolis forces are appreciably affected by the mass and the velocity of the moving load. The response of the system is obtained in terms of Duhamel integral. The differential equation which involves a non-linearity on its right hand side is solved via an iterative procedure. The method has been exemplified for the special values of the variables.