title: Axial-transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions.
abstract: The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.
authors.affiliation: Department of Civil and Buildings Engineering, and Architecture , Polytechnic University of Marche , via Brecce Bianche, 60131 Ancona, Italy.
authors.forename: Stefano
authors.identifier: 0000-0003-3154-7896
authors.initials: S
authors.lastname: Lenci
authors.affiliation: Department of Structural and Geotechnical Engineering , Sapienza University of Rome , via A. Gramsci, 00197 Rome, Italy.
authors.forename: Giuseppe
authors.initials: G
authors.lastname: Rega
keywords: Timoshenko beam; axial–transversal coupling; nonlinear vibrations; perturbation methods