Active control of parametrically excited systems

Abstract

This article discusses active control of parametrically excited systems. Parametric resonance is observed in a wide range of applications and can lead to high levels of unwanted motion. For example, in cable-stayed bridges, the vibration of the deck excites the cables axially, inducing a periodically time-varying tension. If the frequency of deck vibration is about twice the natural frequency of the cable, a parametric resonance occurs and leads to a large-amplitude swinging motion of the cable. To tackle the consequences of parametric instability, active vibration control employing a piezoelectric actuator is proposed in this article. We consider a beam subjected to an axial harmonic load that represents a parametrically excited system with a periodically varying stiffness. Using both analytical and experimental methods, we assess the stability of the beam and propose active control aimed at relocating the transition curves and hence stabilising the system via velocity feedback and pole placement. Analytical relationship between the transition curves and the poles of the system is derived. Transition curves can be assigned to a prescribed location using appropriate velocity and displacement control gains. Finally, we demonstrate the proposed approach with experiments on a beam equipped with a macro fibre composite patch

Improved Modelling of a Nonlinear Parametrically Excited System with Electromagnetic Excitation

“…By reducing the damping, the stability threshold can be reduced. The stability threshold at the parametric resonance can be found from Equations (8) and (9) when nonlinear terms are zero, or by solving Equation (2) using the harmonic balance method [27]. The stability threshold is found to be δ th = 4ζ m .…”

“…Various geometries have been chosen to design NPE oscillators, such as spring mass structures [7], cantilever beams [8], and torsional spring oscillators [9]. The axially driven cantilever beam is extensively used due to its simple geometry, well known analytical model, and ease of fabrication.…”