Axial-transversal coupling in the nonlinear dynamics of a beam with an inclined roller

The nonlinear oscillations of an Euler–Bernoulli beam hinged at one end and having a roller support sliding on a inclined line on the other end are investigated for the first time (to the best of the authors’ knowledge). Free and forced dynamics are studied, and the backbone curve and frequency response curve are obtained by the multiple time scale method. These results allow us to detect analytically the main features of the nonlinear dynamics, in particular the hardening/softening dichotomy, and how it is influenced by the various beam parameters. Furthermore, the analytical results are compared with finite element simulations to check their reliability. The main goal of the paper is that of investigating the coupling between axial and transversal displacements, which appears yet in the linear regime (first order solution) due to the slope of the constraint. An element of novelty consists of showing the qualitative and quantitative changes that the coupling undergoes passing from small (linear regime) to moderate and large (nonlinear regime) displacements.