NON-LINEAR CONTROL OF BUCKLED BEAMS UNDER STEP LOADING

Abstract

The present paper studies a strategy for the active non-linear control of the oscillations of simply supported buckled beams, in order to mitigate the effects of dynamic loading on the vibration amplitudes and prevent dangerous instability phenomena. First, an analysis of the symmetric non-linear behaviour of the structure without any control system is carried out. In order to control the non-linear vibrations of the beam, an active tendon control system is adopted. A control method based on non-linear optimal control using state feedback is developed and the solution of the non-linear optimal control problem is obtained by representing system non-linearities and performance indices by power series with the help of algebraic tensor theory. In this work, general polynomial representations of the non-linear control law are obtained up to the fifth order. This solution procedure is employed to analyse the influence of the resulting non-linear control laws on the dynamic behaviour of a buckled beam under a lateral step load. This arch-like structural system is highly non-linear and under compressive lateral loading may suffer snap-through buckling. This may cause undesirable stresses and/or displacements, leading as a rule to a failure of the structural system. So, special attention is given to the determination of the potential of the present control methodology for efficiently limiting extreme state responses and preventing the snap-through buckling. Numerical results indicate that the control algorithm can effectively increase the load-carrying capacity of the buckled beam without demanding large control forces. Also, this study can be used as a basis for the non-linear control of more complex structures and for the design of control systems.