In-plane free vibration of a pre-stressed curved beam obtained from a large deflected cantilever beam

In this paper, in-plane free vibration of a large deflected cantilever beam fixed at both ends, which forms the case of a pre-stressed curved beam, is investigated. In order to obtain the pre-stressed curved beam case, an external vertical concentrated load is applied at the free end of a cantilever beam and then the loading point of the deflected beam is fixed. The reversion method is used to obtain the non-linear deflection curve of the flexible beam undergoing large deflection. The curved beam is modeled using the finite element method with a straight-beam element approach. The beam is assumed to be an Euler beam. The effects of vertical load on the natural frequency parameter for the first five modes are examined and the results obtained are given in graphics and a table. Moreover, to verify the reliability and validity of the present model, the natural frequency parameters obtained from the present theory are compared with the results obtained from ANSYS software. It has been found that the effect of the load parameter, which forms the curved beam, on the natural frequency parameter almost disappears after a certain value of the load parameter for each vibration mode.