Random Response of Wake-Oscillator Excited by Fluctuating Wind

Many wake-oscillator models applied to study vortex-induced vibration (VIV) are assumed to be excited by ideal wind that is assumed to be uniform flow with constant velocity. While in the field of wind engineering, the real wind generally is described to be composed of mean wind and fluctuating wind. The wake-oscillator excited by fluctuating wind should be treated as a randomly excited and dissipated multi-degree of freedom (DOF) nonlinear system. The involved studies are very difficult and so far there are no exact solutions available. The present paper aims to carry out some study works on the stochastic dynamics of VIV. The stochastic averaging method of quasi integrable Hamiltonian systems under wideband random excitation is applied to study the Hartlen-Currie wake-oscillator model and its modified model excited by fluctuating wind. The probability and statistics of the random response of wake-oscillator in resonant or lock-in case and in non-resonant case are analytically obtained, and the theoretical results are confirmed by using numerical simulation of original system. Finally, it is pointed out that the stochastic averaging method of quasi integrable Hamiltonian systems under wideband random excitation can also be applied to other wake-oscillator models, such as Skop-Griffin model and Krenk-Nielsen model excited by fluctuating wind.

Sasaki–Ricci Flow and Deformations of Contact Action–Angle Coordinates on Spaces T1,1 and Yp,q

In this paper, we are concerned with completely integrable Hamiltonian systems and generalized action–angle coordinates in the setting of contact geometry. We investigate the deformations of the Sasaki–Einstein structures, keeping the Reeb vector field fixed, but changing the contact form. We examine the modifications of the action–angle coordinates by the Sasaki–Ricci flow. We then pass to the particular cases of the contact structures of the five-dimensional Sasaki–Einstein manifolds T1,1 and Yp,q.

Force Evolutionary Billiards and Billiard Equivalence of the Euler and Lagrange Cases

A class of force evolutionary billiards is discovered that realizes important integrable Hamiltonian systems on all regular isoenergy 3-surfaces simultaneously, i.e., on the phase 4-space. It is proved that the well-known Euler and Lagrange integrable systems are billiard equivalent, although the degrees of their integrals are different (two and one).

Normal form for lower dimensional elliptic tori in Hamiltonian systems

<abstract><p>We give a proof of the convergence of an algorithm for the construction of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. The existence of such invariant tori is proved by leading the Hamiltonian to a suitable normal form. In particular, we adapt the procedure described in a previous work by Giorgilli and co-workers, where the construction was made so as to be used in the context of the planetary problem. We extend the proof of the convergence to the cases in which the two sets of frequencies, describing the motion along the torus and the transverse oscillations, have the same order of magnitude.</p></abstract>