Study of the Contribution of Nonlinear Normal Modes (NNMs) in Large Amplitude Oscillations of Simply Supported Beams

This paper focuses on the Nonlinear Normal Modes of simply supported beams with unrestrained axial displacements. Two different configurations are considered, depending on whether longitudinal displacements are allowed at one end of the beam or at both ends. An integro-differential equation is obtained for the transverse displacement of the beam, upon the common assumption of inextensibility. By using a perturbation approach, the NNMs are analytically computed, which yields a frequency-amplitude relation for each NNM. These analytical curves are compared to FE results, showing a remarkable accordance. Noticeably, qualitatively different behaviors are found for the first NNM in both configurations: with one free end, the beam softens; with both ends free, it hardens.