VIBRATION RESPONSE OF A SIMPLY SUPPORTED BEAM SUBJECTED TO A MOVING MASS

An analytical method is presented to determine the dynamic response of a simply supported Euler-Bernoulli beam subjected to a moving mass. The moving mass causes convective acceleration terms in the equation of motion which are not presented when the problem is solved by assuming moving load. These terms change the characteristic of dynamic response of the beam in compared with one subjected to a moving load. First, the equation of motion is achieved by using the assumed modal shape of vibration. The obtained equation consists of perturbed terms. Then, an approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique. It is seen that the convective terms reduce the frequency of the beam-mass system. Also, a numerical method is presented to solve the moving mass problem to validate the results from perturbation technique. Numerical simulations show a fine agreement between the results from analytical and numerical methods

Keywords:

Moving mass , Euler-Bernoulli beam , Perturbation technique , Multiple scales