Nonlinear interaction between self- and parametrically excited wind-induced vibrations

The aeroelastic behavior of a planar prismatic visco-elastic structure, subject to a turbulent wind, flowing orthogonally to its plane, is studied in the nonlinear field. The steady component of wind is responsible for a Hopf bifurcation occurring at a threshold critical value; the turbulent component, which is assumed to be a small harmonic perturbation of the former, is responsible for parametric excitation. The interaction between the two bifurcations is studied in a three-dimensional parameter space, made of the two wind amplitudes and the frequency of the turbulence. Aeroelastic forces are computed by the quasi-static theory. A one-D.O.F dynamical system, drawn by a Galerkin projection of the continuous model, is adopted. The multiple scale method is applied, to get a two-dimensional bifurcation equation. A linear stability analysis is carried out to determine the loci of periodic and quasi-periodic bifurcations. Limit cycles and tori are computed by exact, asymptotic, and numerical solutions of the bifurcation equations. Numerical results are obtained for a sample structure, and compared with finite-difference solutions of the original partial differential equation of motion.

Effectiveness Comparison of Supporting Surfaces in The Ball System for Vibration Isolation of High-Rise Buildings

The mechanical system «a hard homogeneous ball» between the movable upper and lower supports is considered. Its dynamic equations by plane motions are obtained under the action of an external harmonic perturbation. Various cases of support surfaces are considered.

Characterizing the Dynamics of the Watt Governor System Under Harmonic Perturbation and Gaussian Noise

We investigate the disturbance on the dynamics of a Watt governor system model due to the addition of a harmonic perturbation and a Gaussian noise, by analyzing the numerical results using two distinct methods for the nonlinear dynamics characterization: (i) the well-known Lyapunov spectrum, and (ii) the 0-1 test for chaos. The results clearly show that for tiny harmonic perturbations only the smallest stable periodic structures (SPSs) immersed in chaotic domains are destroyed, whereas for intermediate harmonic perturbation amplitudes there is the emergence of quasiperiodic motion, with the existence of typical Arnold tongues and, the consequent distortion of the SPSs embedded in the chaotic region. For large enough harmonic perturbations, the SPSs immersed in chaotic domains are suppressed and the dynamics becomes essentially chaotic. Regarding the noise perturbations, it is able to suppress periodic motion even if tiny noise intensities are considered, as analyzed by a periodic attractor subject to different noise intensities. The threshold of noise amplitude for chaos generation in periodic structures is reported by both methods. Additionally, we investigate the robustness of the 0-1 test for chaos characterization in both noiseless and noise cases, and for the first time, we compare the Lyapunov exponents and 0-1 test methods in the parameter-planes. Our findings are generic due to their remarkable agreement with results previously reported for dynamical systems in other contexts.

Influence of Harmonic Perturbation on Speed of Billiard Particle as Combination of Deterministic Acceleration and White Noise

Chaotic system under influence of harmonic force is considered. Namely, the motion of Fermi-accelerated billiard particles interacting with scatterers with harmonically oscillating boundaries is investigated. The domain of main parameters in which the acceleration of particles does not depend on the period of scatterers oscillations is found. In this domain, the effect of such oscillations can be considered as an impact of white Gaussian noise whose intensity depends only on the amplitude of velocity of scatterer oscillations and the mean free path of particles. The results of numerical simulations are in good agreement with the results of analytical considerations.

Experimental and LES Analysis of a Premix Swirl Burner Under Acoustic Excitation

The frequency response to acoustic excitation of turbulent premixed flames stabilized in a high swirl flow is investigated with high speed diagnostics and Large Eddy Simulation (LES). In both cases, the flame transfer function (FTF), i.e. the frequency response of the total heat release, is also determined. Both experiments and LES show distributions of the FTF amplitude and phase which are different from flames stabilized in non swirling flows, for example piloted conical premixed flames. In order to shed light on these differences, the effect on the FTF of the swirl velocity fluctuation driven by a forced harmonic perturbation in the reactant flow rate is isolated in the LES simulations using a novel methodology that makes use of the Proper Orthogonal Decomposition (POD). The typical FTF distributions observed in experiments for swirl stabilized flames are interpreted on the basis of this separation. A close link with the frequency response of the velocity field distribution in the combustor is also established.