Vortex-induced vibration of a circular cylinder with nonlinear stiffness: prediction using forced vibration data

Nonlinear Dynamics - Vortex-induced vibration (VIV) systems with stiffness nonlinearity have received increasing attention because the stiffness nonlinearity can broaden the effective flow velocity...     

Weighted Dunkl transform inequalities and application on radial Besov spaces

In Dunkl theory on $\mathbb R ^d$ which generalizes classical Fourier analysis, we prove first weighted inequalities for certain Hardy-type averaging operators. In particular, we deduce for specific choices of the weights the $d$ -dimensional Hardy inequalities whose constants are sharp and independent of $d$ . Second, we use the weight characterization of the Hardy operator to prove weighted Dunkl transform inequalities. As consequence, we obtain Pitt’s inequality which gives an integrability theorem for this transform on radial Besov spaces.     

Electrical conductivity and complex impedance analysis of 20% Ti-doped La0.7Sr0.3MnO3 perovskite

The electrical conductance of 20% Ti-doped La_0.7Sr_0.3MnO₃ (LSMO) was measured using admittance spectroscopy over a wide temperature and frequency ranges. The impedance plane plot shows semicircle arcs at different temperatures and an electrical equivalent circuit has been proposed to explain the impedance results. Activation energy inferred from conductance spectrum matches very well with the value estimated from relaxation time indicating that relaxation process and conductivity have the same origin. The electrical conductance of La_0.7Sr_0.3Mn_0.8Ti_0.2O₃ is found to be dependent on temperature and frequency. Also, the electronic conduction appears to be dominated by thermally activated hopping of small polaron (SPH) at high temperatures and by variable range hopping (VRH) at low temperatures.     

Performance enhancement of wing-based piezoaeroelastic energy harvesting through freeplay nonlinearity

We investigate experimentally how controlled freeplay nonlinearity affects harvesting energy from a wing-based piezoaeroelastic energy harvesting system. This system consisits of a rigid airfoil which is supported by a nonlinear torsional spring (freeplay) in the pitch degree of freedom and a linear flexural spring in the plunge degree of freedom. By attaching a piezoelectric material (PSI-5A4E) to the plunge degree of freedom, we can convert aeroelastic vibrations to electrical energy. The focus of this study is placed on the effects of the freeplay nonlinearity gap on the behavior of the harvester in terms of cut-in speed and level of harvested power. Although the freeplay nonlinearity may result in subcritical Hopf bifurcations (catastrophic for real aircrafts), harvesting energy at low wind speeds is beneficial for designing piezoaeroelastic systems. It is demonstrated that increasing the freeplay nonlinearity gap can decrease the cut-in speed through a subcritical instability and gives the possibility to harvest energy at low wind speeds. The results also demonstrate that an optimum value of the load resistance exists, at which the level of the harvested power is maximized.     

Multi-scroll and multi-wing chaotic attractor generated with Julia process fractal

This paper proposes a general multi-scrolls and multi-wings attractor systems while combining in one hand, Julia’s process with Lorenz’s attractor and in another hand Julia’s process with two coupled Lorenz systems. We have also studied the combination of Julia’s process with the chaotic attractor system proposed in [1].     

An analytical and experimental investigation into limit-cycle oscillations of an aeroelastic system

We perform an analytical and experimental investigation into the dynamics of an aeroelastic system consisting of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom and a nonlinear spring in the pitch degree of freedom. The experimental results show that the onset of flutter takes place at a speed smaller than the one predicted by a quasi-steady aerodynamic approximation. On the other hand, the unsteady representation of the aerodynamic loads accurately predicts the experimental value. The linear analysis details the difference in both formulation and provides an explanation for this difference. Nonlinear analysis is then performed to identify the nonlinear coefficients of the pitch spring. The normal form of the Hopf bifurcation is then derived to characterize the type of instability. It is demonstrated that the instability of the considered aeroelastic system is supercritical as observed in the experiments.     

Bifurcation analysis of an aeroelastic system with concentrated nonlinearities

Analytical and numerical analyses of the nonlinear response of a three-degree-of-freedom nonlinear aeroelastic system are performed. Particularly, the effects of concentrated structural nonlinearities on the different motions are determined. The concentrated nonlinearities are introduced in the pitch, plunge, and flap springs by adding cubic stiffness in each of them. Quasi-steady approximation and the Duhamel formulation are used to model the aerodynamic loads. Using the quasi-steady approach, we derive the normal form of the Hopf bifurcation associated with the system??s instability. Using the nonlinear form, three configurations including supercritical and subcritical aeroelastic systems are defined and analyzed numerically. The characteristics of these different configurations in terms of stability and motions are evaluated. The usefulness of the two aerodynamic formulations in the prediction of the different motions beyond the bifurcation is discussed.     

On the onset of bifurcation and nonlinear characterization of vortex-induced vibrations under varying initial conditions

Nonlinear Dynamics - We perform numerical simulations to investigate the hysteresis phenomenon near the bifurcation points of the synchronization region leading to vortex-induced vibrations. We...