Determining the effect of detuning parameters on the absorption region for a coupled nonlinear system of varying orientation

In this study, the nonlinear behavior of a slender beam coupled with a pendulum is investigated numerically in terms of different system parameters. The structure consisting of a cantilever beam of varying orientation with a tip mass and pendulum which is attached to the tip mass as a passive vibration absorber is subjected to a vertical sinusoidal base excitation. The Euler–Bernoulli theory for the slender beam is used to derive the governing non-linear partial differential equation. The non-linear terms arising from inertia, curvature and axial displacement caused by large transverse deflections, and the coupling between the primary structure and absorber are retained up to third order. When the structure is forced in the neighborhood of its resonance, the pendulum absorber (controller) reduces the structure response because of autoparametric interaction between the beam and pendulum. Autoparametric interaction in the system was investigated by varying orientation angles, the forcing amplitude, the internal frequency ratio, and the mass ratio in the neighborhood of the autoparametric resonance. The absorption regions were defined with respect to the system parameters for the passive vibration absorber.