Nonregular Regimes of Monodimensional Mechanical Systems with Initial Curvature: Experiments and Time Series Analysis

Abstract

The 3D finite dynamics of monodimensional elastic structures with initial curvature is particularly rich and varied because of the presence of both even and odd nonlinearities, the former being directly linked to the initial curvature [1]. This work is concerned with the analysis of experimental models of two different systems belonging to that class. The first is a discrete model of an elastic suspended cable excited by vertical, sinusoidally varying, motion of the hanging points. The second is a steel model of a double hinged circular arch excited by a vertical, sinusoidally varying, concentrated force at its tip. In strongly developed nonlinear regimes, interesting phenomena linked to the nonlinear modal interaction appear in such systems over a wide range of excitation frequencies, owing to the very close sequence of primary and secondary resonance conditions. Moreover, changing the sag to span ratio of the cable or adding a vertical dead load on the tip of the arch it is possible to obtain various internal resonance conditions which further exhalt those nonlinear interaction phenomena.