Modal Interactions and Time Delay Control of a Parametrically Excited Nonlinear Composite Column

Abstract

Modal interactions, stability analysis and time delay control of a composite column loaded by axial periodic force is presented in the paper. The simply supported column is composed of channel sections made of layers of a laminate with an arrangement which couples bending and twisting of the structure. The laminate coupling, together with a nonlinear geometrical displacement field result in a nonlinear model with parametric excitation. It is shown that for the selected configuration different mode couplings and parametric instability zones may occur. In order to stabilise the system a time delay displacement feedback control is proposed. An effect of the time delay control on the first principal parametric resonance zone is studied analytically and numerically.