Vibration analysis of beams with intermediate supports under moving loads

Abstract

In this study, transverse vibration of a beam under a moving singular load and a moving moment is investigated. A simply supported beam with intermediate vertical supports modeled according to Euler-Bernoulli beam theory. The intermediate supports are modeled as consisting of a linear spring and a linear damper. The moving force and the moment, the spring force and the damper force are expressed using Dirac delta functions in the equations of motion. Obtaining the exact solution for this problem with classical methods are quite lengthy and complicated. Beam must be divided into spans between each support. Each span must be solved separately with different set of coordinates having same boundary conditions on support points. As the number of support increases, solution becomes more complicated. However, the present method can be used to solve the problem for the whole beam length without having to separate into various spans regardless of number of supports. Dirac delta functions are converted to series expansions which allows us to get exact solution in form of series expansion. This solution than can be easily calculated by a computer. Dynamic responses of several cases such as various number of supports; different support points; various moving load, moving moment and axial load combinations are examined.