Design Procedure of a Nonlinear Vibration Absorber Using Bifurcation Analysis

A nonlinear energy sink (NES) is characterized by its ability to passively realize targeted energy transfer as well as multimodal damping. This latter feature seems to make this device very well suited for reducing the vibration level of MDOF linear structures. The perspective of dealing with MDOF linear primary structures requires the development of an efficient NES design procedure. This paper poses the basis of such a procedure based upon the bifurcation analysis of a system composed of a linear oscillator coupled to a NES, using the software MatCont

Vandalism Prevention of a Footbridge with Cable Vibrations

peer reviewedThis work studies an unusual way to improve comfort of a footbridge with cables. Cables can be seen as a means of dissipating energy in a structure. This complementary source of dissipation does not prohibit resonance from taking place, but it is a way to limit vibrations and to impede vandals’ actions. This study is illustrated with measurements realized on a specific footbridge. This structure is a metallic arch characterized by a first natural frequency of 3.2Hz and a corresponding damping ratio of 0.55%. Intolerable accelerations (around 6m/s²) are easily reached when an ill-intentioned person is bouncing at an appropriate frequency. After installation of a single cable at a suitable location in the structure, the measured damping ratios are almost doubled and the maximum accelerations at resonance are reduced by 30%. With three cables on the footbridge, the damping ratio becomes significantly nonlinear: it reaches up to 3% for low amplitude oscillations, but drops down to 1% for moderate to high amplitudes. For higher accelerations, it does not seem to depend on the number of cables. According to these observations, a notable effect of cables is to reduce the maximum acceleration, but the main effect is to prolong the transient phase and to make the resonance frequency hardly identifiable by vandals

Onset and stabilization of delay-induced instabilities in piezoelectric digital vibration absorbers

The stability of a piezoelectric structure controlled by a digital vibration absorber emulating a shunt circuit is investigated in this work. The formalism of feedback control theory is used to demonstrate that systems with a low electromechanical coupling are prone to delay-induced instabilities entailed by the sampling procedure of the digital unit. An explicit relation is derived between the effective electromechanical coupling factor and the maximum sampling period guaranteeing a stable controlled system. Since this sampling period may be impractically small, a simple modification procedure of the emulated admittance of the shunt circuit is proposed in order to counteract the effect of delays by anticipation. The theoretical developments are experimentally validated on a clamped-free piezoelectric beam

Chattering-free Sliding Mode Control for Propellantless Rendez-vous using Differential Drag

peer reviewedThis paper develops a differential drag-based sliding mode controller for satellite rendez-vous. It is chattering-free and avoids bang-bang type control to adjust the relative motion more efficiently. In spite of uncertain nonlinear perturbations and disturbances, it is shown that the in-plane relative motion between two satellites can be effectively controlled by regulating the drag difference. An adaptive tuning rule is also presented such that the errors are suppressed to lie within a desired error box. The proposed controller is simple and easy to implement in a small satellite, and numerical simulations are carried out to demonstrate its effectiveness in a high fidelity environment

Flutter and limit cycle oscillation suppression using linear and nonlinear tuned vibration absorbers

Aircraft are more than ever pushed to their limits for performance reasons. Consequently, they become increasingly nonlinear and they are more prone to undergo aeroelastic limit cycle oscillations. Structural nonlinearities affect aircraft such as the F-16, which can undergo store-induced limit cycle oscillations (LCOs). Furthermore, transonic buzz can lead to LCOs because of moving shock waves in transonic flight conditions on many aircraft. This study presents a numerical investigation of passive LCO suppression on a typical aeroelastic system with pitch and plunge degrees of freedom and a hardening stiffness nonlinearity. The absorber used is made of a piezoelectric patch glued to the plunge springs and connected to a resistor and an inductance forming a RLC circuit. A mechanical tuned mass damper absorber of similar configuration is also considered. The piezoelectric absorber features significant advantages in terms of size, weight and tuning convenience. The results show that both types of absorber increase the linear flutter speed of the system in a similar fashion but, when optimal, they lead to a sub-critical bifurcation while a super-critical bifurcation was observed without absorber. Finally, it is shown that the addition of a properly tuned nonlinear spring (mechanical absorber) or capacitor (piezo- electric absorber) can restore the super-criticality of the bifurcation. The tuning of the nonlinearity is carried out using numerical continuation.The nonlinear tuned vibration absorber (NoVib 307265

Passive Linearization of Nonlinear System Resonances

In this work we demonstrate that the addition of properly-tuned nonlinearities to a nonlinear system can increase the range over which a specific resonance responds linearly. Specifically, we seek to enforce two important properties of linear systems, namely the force-displacement proportionality and the invariance of resonance frequencies. Theoretical findings are validated through numerical simulations and experiments

Identification of complex nonlinearities using cubic splines with automatic discretization

One of the major challenges in nonlinear system identification is the selection of appropriate mathematical functions to model the observed nonlinearities. In this context, piecewise polynomials, or splines, offer a simple and flexible representation basis requiring limited prior knowledge. The generally-adopted discretization for splines consists in an even distribution of their control points, termed knots. While this may prove successful for simple nonlinearities, a more advanced strategy is needed for nonlinear restoring forces with strong local variations. The present paper specifically introduces a two-step methodology to select automatically the location of the knots. It proposes to derive an initial model, using nonlinear subspace identification, and incorporating cubic spline basis functions with fixed and equally-spaced abscissas. In a second step, the location of the knots is optimized iteratively by minimizing a least-squares cost function. A single-degree-of-freedom system with a discontinuous stiffness characteristic is considered as a case study

Experimental Characterization of Superharmonic Resonances Using Phase-Lock Loop and Control-Based Continuation

Experimental characterization of nonlinear structures usually focuses on fundamental resonances. However, there is useful information about the structure to be gained at frequencies far away from those resonances. For instance, non-fundamental harmonics in the system's response can trigger secondary resonances, including superharmonic resonances. Using the recently-introduced definition of phase resonance nonlinear modes, a phase-locked loop feedback control is used to identify the backbones of even and odd superharmonic resonances, as well as the nonlinear frequency response curve in the vicinity of such resonances. When the backbones of two resonances (either fundamental or superharmonic) cross, modal interactions make the phase-locked loop unable to stabilize some orbits. Control-based continuation can thus be used in conjunction with phase-locked loop testing to stabilize the orbits of interest. The proposed experimental method is demonstrated on a beam with artificial cubic stiffness exhibiting complex resonant behavior. For instance, the frequency response around the third superharmonic resonance of the third mode exhibits a loop, the fifth superharmonic resonance of the fourth mode interacts with the fundamental resonance of the second mode, and the second superharmonic resonance of the third mode exhibits a branch-point bifurcation and interacts with the fourth superharmonic resonance of the fourth mode

Experimental Passive Flutter Mitigation Using a Linear Tuned Vibrations Absorber

The current drive for increased efficiency in aeronautic structures such as aircraft, wind turbine blades and helicopter blades often leads to weight reduction. A consequence of this tendency can be increased flexibility, which in turn can lead to unfavourable aeroelastic phenomena involving large amplitude oscillations and nonlinear effects such as geometric hardening and stall flutter. Vibration mitigation is one of the approaches currently under study for avoiding these phenomena. In the present work, passive vibration mitigation is applied to an experimental aeroelastic system by means of a linear tuned vibration absorber. The aeroelastic apparatus is a pitch and flap wing that features a continuously hardening restoring torque in pitch and a linear one in flap. Extensive analysis of the system with and without absorber at subcritical and supercritical airspeeds showed an improvement in flutter speed around 34%, a suppression of a jump due to stall flutter, and a reduction in LCO amplitude. Mathematical modelling of the experimental system showed that optimal flutter delay can be obtained when two of the system modes flutter simultaneously. However, the absorber quickly loses effectiveness as it is detuned. The wind tunnel measurements showed that the tested absorbers were much slower to lose effectiveness than those of the mathematical predictions