Bifurcation and chaos of an articulated loading platform with piecewise non-linear stiffness using the incremental harmonic balance method

Abstract

The bifurcation behavior of an articulated loading platform subjected to harmonic excitation is investigated by the incremental harmonic balance (IHB) method. The platform is modeled as a single-degree-of-freedom (SDOF) non-linear system with piecewise non-linear restoring force characteristics. The elements of the Jacobian matrix and the residue vector arising in the IHB formulations are derived in closed form. The path-following procedure using the arc length continuation method is used to trace the response curves and bifurcation diagrams. The periodic solutions and the subharmonic solutions obtained by the IHB method compare very well with the numerically integrated solutions. The bifurcation points also compare well with the numerically obtained results. The system exhibits chaotic motion through a sequence of period doubling bifurcations. Isolated period 3 solutions are also present. The Lyapunov exponents are computed and the initial condition map corresponding to coexistent attractors are obtained by the interpolated cell mapping (ICM) method.