A novel nonlinear oscillator consisting torsional springs and rigid rods

Abstract

In this paper, we propose an archetypal double-winged novel nonlinear oscillator composed of torsional springs and rigid rods which behaves smooth and discontinuous dynamics and a kind of special collision pendulum depending on the varying of a geometrical parameter. The system behaves complicated equilibrium bifurcations with different geometrical states, leading to a series of buckling phenomenon and the loss of uniqueness near the limit points. A ‘collision’ parameter is introduced to determine the motions near the limit points which causes a discontinuous jump of velocity and exhibits the standard dynamics as an inverted pendulum, even though the mechanic model is rather different from a pendulum. We also distinguish the coexistence of periodic and chaotic motions and also a smooth period 1 located in a small region under the presence of damping and external force using amplitude–frequency analysis and numerical simulations. This research enriches the complicated dynamical behaviors of geometrical nonlinear oscillator and provide a novel structure which is of great potential in vibration isolation engineering.