Nonlinear vibration of beams under nonideal boundary conditions

In this paper, we investigate the influence of nonideal boundary conditions on the nonlinear vibration of damped Euler–Bernoulli beams subjected to harmonic loads. These nonidealities allow for small deflections and/or moments at the supports of the beam. Using the iteration perturbation method, analytical expressions for the case of simply supported beams with immovable end conditions are provided. The results reveal that the first order of approximation obtained by the proposed method is more accurate than the perturbation solutions. Moreover, compared with the previous studies, some interesting phenomenon is predicted. We have shown that in some special combinations of the nonidealities the nonlinear frequency of vibration as well as the frequency–response curves would be unchanged.