DICEAA

A method to design semi-active control strategies of asymmetric structures is presented. The method is based on the optimal sizing of an equivalent Kelvin-Voight model describing the constitutive behavior of semi-active magneto-rheological devices, through the evaluation of the maximum achievable modal damping when they work in passive modality. The complex eigenvalue loci of the passively-controlled system versus the device mechanical characteristics are spanned for symmetric and asymmetric frame structures. A coherent representation of the reference effect ensured by an optimized linear active feedback on the eigenvalues loci is selected to drive the design of the adjustable properties of the semi-active device. A clipped-optimal control algorithm is used in a prototype experimental application whose performance are highlighted by the presented design method.

Thefeasibility of reducing vibrations in suspended cables by animposed longitudinal displacement of one support is investigatedthrough an analytical model. A noncollocated active control schemeis considered where modal amplitudes describing transverse oscillationsare used in the feedback control action at the boundary. A 2DOFnonlinear model of the cable is used to design state-feedbackcontroller. Linear and nonlinear velocity feedback and feedbackbilinearisation are shown to produce a nonlinear and bilinearactively-damped system, respectively. The controlled system performanceis analysed comparing the effectiveness of the different strategieson both control demand and response amplitudes in the stabilizationof the equilibrium position. Control spillover effects are commentedthrough an enlarged 8DOF modal description of the controlledcable oscillations.

The governing equations for dynamic transverse motion of a cable-stayed beam are obtained by means of a classical variational formulation. The analytical model permits a parametric investigation of linear and non-linear behaviour in a family of cable-stayed beam systems. Analytical eigensolutions of the linearized equations are used to investigate how the mechanical characteristics influence the occurrence of global, local and coupled modes. The exact eigenfunctions are assumed to describe the forced harmonic motion in the neighbourhood of a selected frequency. The frequency–amplitude relationship, obtained by the use of the multiple scale method, permits the description of softening and hardening behaviour in the global, local and coupled classes of motion. Copyright © 2002 John Wiley & Sons, Ltd

Abstract. Active control of oscillations of a suspended cable under transversal wind, described by a constant term and a fluctuating turbulent component, is dealt with. Control of transversal in-plane and out-of-plane oscillations is performed by imposing a longitudinal motion to one support; the control law depends, linearly or quadratically, on measures of displacement and velocity of a selected point. First, the steady-state oscillations around the planar static configuration, determined by the wind constant component, under sinusoidal in-plane and out-of-plane loading are studied, showing the nonlinear behaviour in the regions of primary and parametric resonance and the effects of the control action. Afterwards, attention is focused on the response of the cable to transversal wind turbulence, whose fluctuating component is described by a random process with an assigned spectral density. The effectiveness of longitudinal control is analysed by means of numerical investigations. Sommario. Si analizza il controllo attivo delle oscillazioni di un cavo sospeso, sottoposto all'azione di un vento agente in direzione ortogonale al piano del cavo e descritto mediante un termine di carico costante ed una componente variabile di turbolenza. Il controllo delle oscillazioni piane e spaziali viene realizzato mediante spostamento longitudinale di uno degli appoggi; la legge di controllo dipende linearmente o quadraticamente da misure di spostamento e velocità di un punto prescelto. In una prima fase, vengono studiate le oscillazioni stazionarie sotto carichi sinusoidali agenti rispettivamente nel piano e fuori del piano del cavo, intorno alla configurazione di equilibrio statico determinata dalla presenza della componente costante del vento, mostrando il comportamento nonlineare nelle regioni di risonanza primaria e parametrica e gli effetti dell'azione di controllo. Successivamente, si focalizza l'attenzione sulla risposta del cavo alla componente trasversale di turbolenza del vento, la quale è descritta da un processo stocastico a media nulla con densità spettrale assegnata. L'efficacia del controllo viene analizzata attraverso un'indagine numerica.

The nonlinear oscillations of a controlled suspended elastic cable under in-plane excitation are considered. Active control realized by longitudinal displacement of one support is introduced in order to reduce the transverse in-plane and out-of-plane vibrations. Linear and quadratic enhanced velocity feedback control laws are chosen and their effects on the cable motion are investigated using a two degree-of-freedom model. Perturbation analysis is performed to determine the in-plane steady-state solutions and their stability under an out-of-plane disturbance. The analysis is extended to the bifurcated two-mode steady-state oscillations in the region of parametric excitation. The dependence of the control effectiveness on the system parameters is investigated in the case of the first symmetric mode and the range of oscillation amplitudes in which the proposed control ensures a dissipation of energy is determined. Although control based only on in-plane response quantities is effective in reducing oscillations with a prevailing in-plane component, addition of out-of-plane measures has to be considered when the motion is characterized by two comparable components.