DYNAMIC STABILITY AND CHAOS OF SYSTEM WITH PIECEWISE-LINEAR STIFFNESS

The dynamic stability behavior of a single-degree-of-freedom system wi th piecewise linear stiffness is considered. The analytical expression representing the divergence of perturbed trajectories is derived. The mechanism triggering dynamic instability of trajectories and the caus e of chaotic behavior are then studied. Liapunov exponents are used as a quantitative measure of system stability. Numerical results includi ng bifurcation diagrams and largest Liapunov exponents of a system wit h symmetric bilinear stiffness are presented. Several different types of bifurcation and nonlinear phenomena are identified, including pitch fork, fold, flip, boundary crisis, and intermittency of type 3. To ill ustrate the initial-condition dependent nature of the problem, basins of attraction of multiple steady-state responses are determined on the phase plane using the simple cell mapping method.