Dynamic analysis of an inclined beam due to moving loads

It has been found that if each of the moving loads on the beam is considered as a moving mass element, then one can easily formulate the problem with all the pertinent factors relating to the multiple moving loads considered. To this end, the property matrices of the moving mass element are derived by taking account of the effects of inertial force, Coriolis force and centrifugal force induced by the moving mass. Combination of the element property matrices for each of the moving loads and the associated overall property matrices for the inclined beam itself determines the overall effective property matrices of the entire vibrating system. Since the property matrices of each moving mass element are dependent on the instantaneous position of the moving load on the inclined beam, they are time-dependent and so are the overall effective mass, damping and stiffness matrices of the entire vibrating system. To validate the presented theory, the dynamic responses of a horizontal pinned-pinned beam subjected to a moving load are determined and compared with those of the existing literature and good agreement is achieved. Finally, the following factors having something to do with the title problem are studied: the moving-load speed, the Coriolis force, centrifugal force, the frictional force, the inclined angle of the beam and the total number of moving loads. Numerical results reveal that all the above-mentioned parameters have significant influence on both the vertical (y¯) and the horizontal (x¯) dynamic responses of the inclined beam except the frictional force.