FREE VIBRATION OF A SIMPLY SUPPORTED BEAM UNDER A NON-CONSERVATIVE DISTRIBUTED LOAD

The free vibration of post-buckling beams subjected to non-conservative load is studied. Based on the large deformation theory for the elastic beams, the geometrically nonlinear dynamic equations are established for beams subjected to a distributed tangential follower force along the central axis. By assuming that the amplitude of beam's vibration is small and its response harmonic, a linear version of the vibration problem is deduced. By employing the numerical shooting technique to solve the governing equations for vibration, numerical solutions of the first three natural frequencies against the load parameter are obtained. The results show that the features of the vibration response of the beams subjected to a non-conservative load are evidently different from those subjected to a conservative load.