STABILITY, BIFURCATION AND CHAOS OF NONLINEAR STRUCTURES WITH CONTROL .1. AUTONOMOUS CASE

We study a class of structural models with non-linear soft spring and active control subjected to simple harmonic excitations. The first of the two parts deals with the analysis of stability and bifurcations of the autonomous (or unforced) system, using the basic concept of Liapunov exponent, the center manifold theorem, normal forms, the Melnikov method, the Bendixon criterion and perturbation methods. Regions of stability and bifurcation sequences in the parameter space of the system are obtained analytically along with those by numerical simulations. Part II of our study concentrates on the analysis of stability and chaos of the non-autonomous (or forced) system.