Vincenzo Gattulli

Nonlinear interactions in the planar dynamics of cable-stayed beam

Abstract An analytical model is proposed to study the nonlinear interactions between beam and cable dynamics in stayed-systems. The integro-differential problem, describing the in-plane motion of a simple cable-stayed beam, presents quadratic and cubic nonlinearities both in the cable equation and at the boundary conditions. Mainly studied are the effects of quadratic interactions, appearing at relatively low oscillation amplitude. To this end an analysis of the sensitivity of modal properties to parameter variations, in intervals of technical interest, has evidenced the occurrence of one-to-two and two-to-one internal resonances between global and local modes. The interactions between the resonant modes evidences two different sources of oscillation in cables, illustrated by simple 2dof discrete models. In the one-to-two global–local resonance, a novel mechanism is analyzed, by which cable undergoes large periodic and chaotic oscillations due to an energy transfer from the low-global to high-local frequencies. In two-to-one global–local resonance, the well-known parametric-induced cable oscillation in stayed-systems is correctly reinterpreted through the autoparametric resonance between a global and a local mode. Increasing the load the saturation of the global oscillations evidences the energy transfer from high-global to low-local frequencies, producing large cable oscillations. In both cases, the effects of detuning from internal and external resonance are presented.

Nonlinear Oscillations of a Nonresonant Cable under In-Plane Excitation with a Longitudinal Control

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.

One to one resonant double Hopf bifurcation in aeroelastic oscillators with tuned mass dampers

The effects of a tuned added mass on the aeroelastic stability of a single degree of freedom bluff body exposed to a steady flow are investigated. The model captures the essential aspects of the behaviour of flexible structures equipped with Tuned Mass Dampers undergoing galloping oscillations. The system exhibits simple as well double Hopf bifurcations, of non-resonant and 1:1 resonant type. Postcritical behaviour of the system in the neighbourhood of the 1:1 resonant type bifurcation is investigated. Employing the Multiple Scale Method, a second order bifurcation equation in the complex amplitude of motion is obtained. Analytical solutions are used to describe the bifurcation scenario in the cases of both undercritical and supercritical aerodynamic behaviour of the bluff body. The effectiveness of the Tuned Mass Damper even in the postcritical range is proved.

Adaptive control of flow-induced oscillations including vortex effects

Abstract Flow-induced vibrations constitute important design criteria for most offshore structures as well as for many other structures subjected to flow-induced forces. Both the main structural elements as well as supporting structural members such as guyed cables must be designed to withstand such oscillations. It is well established that in the process of vibrations induced by flow, vortices form around the body which initiate oscillations in a direction transverse to the general direction of motion. In this paper, Morison’s equation is used to represent the interaction between the flow field and the structure, complemented by terms including the vortex dynamics effect. In order to mitigate against extreme vibration conditions, here, the implementation of active control is proposed to stabilize the motion of a structure immersed in a flow field. Specifically, a tuned mass damper is attached to the structure and adaptive control is utilized for moving the mass along a particular path while allowing for uncertainty in the various hydrodynamic coefficients. The proposed procedure have two distinct beneficial results. The first one being to control the vibration of the structure, and the second one is the estimation of the hydrodynamic coefficients and the validation/calibration of Morison’s equation model for the flow-induced forces.

Damage Identification in Elastic Suspended Cables through Frequency Measurement

Structural cables in cable-stayed systems are subject to potential damage, mainly due to fatigue phenomena and galvanic corrosion. The paper analyzes how the dynamical behavior of cables is affected by diffuse damage, and investigates whether the damage can be identified through information selected from the dynamical response. A continuous monodimensional model of a damaged cable is used for this purpose. Damage is described as a reduction of the cable cross section, and defined in terms of its intensity, extent and position. The major effects of these different damage parameters on the cable static response and spectral properties are evidenced and discussed to verify the observability of the damage. The frequencies of the dominant transversal motion of the cable are chosen as damage indicators, since they are sufficiently sensitive to the damage intensity and extent, while the damage position requires additional information. The damage identification problem is formulated by defining an objective error function between the measured and the model frequencies, to be minimized in the space of the damage parameters. Pseudo-experimental data are initially used to test the effectiveness and resolution of the procedure. The results confirm the uniqueness of the problem solution and its correctness. The robustness of the solution is discussed while considering the presence of random errors of increasing amplitude. The procedure is also positively verified with experimental measures from a prototype model of an artificially damaged spiral strand.

An Integrated Approach to the Design of Wireless Sensor Networks for Structural Health Monitoring

Wireless Sensor Networks are a promising technology for the implementation of Structural Health Monitoring systems, since they allow to increase the diffusion of measurements in the structure and to reduce the sensor deployment effort and the overall costs. In this paper, possible benefits and critical issues related with the use of Wireless Sensor Networks for structural monitoring are analysed, specifically addressing network design strategies oriented to the damage detection problem. A global cost function is defined and used for the definition of possible design methodologies. Among the various approach, the use of an integrated strategy, able to take advantage of a preliminary structural analysis is considered. Moreover, the implementation of a distributed processing is an explored strategy for an overall improvement of system performances. Benefits of this methodology are finally demonstrated through the analysis of a representative case study, the IASC-ASCE benchmark problem.

Nonlinear strategies for longitudinal control in the stabilization of an oscillating suspended cable

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.

Planar Motion of a Cable-Supported Beam with Feedback Controlled Actions

Active tendon control for slender and flexible structural systems such as guyed mast and cable-stayed bridge, is an innovative methodology to contain their oscillations. In this paper, a simple cable-supported cantilever beam is controlled by means of an imposed longitudinal displacement at the grounded end of the cable aiming to stabilize planar oscillation amplitudes of both cable and beam. The equations of motion of this system are obtained including cable elasticity through finite strain. Analytical eigensolutions of the linearized equations are used to investigate influences of mechanical characteristics on a family of structural systems and to derive a nonlinear discrete model by classical Galerkin method. A one mode model is used to design linear and nonlinear feedback control laws. Comparisons on the effectiveness of different strategies are made on the basis of both control intensity and system response amplitudes.

Serviceability and Damage Scenario in Irregular RC Structures: Post-Earthquake Observations and Modeling Predictions

AbstractThe catastrophic earthquake that struck the city of L’Aquila in early April 2009 caused extensive damage to buildings at the University of L’Aquila. Among these edifices are those of the Engineering Faculty, which, in particular, suffered large structural displacements and accelerations that resulted in failures of nonstructural elements (infills, false ceilings, door and window frames), the breakage of wiring and piping systems, and the destruction of furniture and machinery. Of these buildings, the so-called Edifice A presents the most critical damage scenario, requiring a significant rehabilitating intervention. The structural behavior of this building, composed of seven independent RC substructures, is the object of intensive investigation; this is in part because irregularities among these substructures, in terms of geometry, stiffness, and weight distribution, provide a rich case study for interpreting different structural and nonstructural damage scenarios. The paper interprets the observed...

Retrofitting Effects On The Dynamic Behaviour Of S.Maria Di Collemaggio

The Basilica S.Maria di Collemaggio has recently been subjected to some smallscale repair work required after a recent earthquake in Central Italy; the structure has also been moderately strengthened. As preliminary step, a numerical analysis to predict and frame the effects of the work was performed by finite element models. Experimental research was also conducted to help calibrate the parameters of numerical models and, at the same time, to verify the actual behaviour of the church before and after reinforcement. The numerical and experimental analyses compared in this paper allow us to assess the consequences of the reinforcement and to appreciate the effectiveness of dynamic tests.