Periodically Forced Nonlinear Oscillators With Hysteretic Damping

We perform a detailed study of the dynamics of a nonlinear, one-dimensional oscillator driven by a periodic force under hysteretic damping, whose linear version was originally proposed and analyzed by Bishop in [1]. We first add a small quadratic stiffness term in the constitutive equation and construct the periodic solution of the problem by a systematic perturbation method, neglecting transient terms as $t\rightarrow \infty$. We then repeat the analysis replacing the quadratic by a cubic term, which does not allow the solutions to escape to infinity. In both cases, we examine the dependence of the amplitude of the periodic solution on the different parameters of the model and discuss the differences with the linear model. We point out certain undesirable features of the solutions, which have also been alluded to in the literature for the linear Bishop's model, but persist in the nonlinear case as well. Finally, we discuss an alternative hysteretic damping oscillator model first proposed by Reid [2], which appears to be free from these difficulties and exhibits remarkably rich dynamical properties when extended in the nonlinear regime.Comment: Accepted for publication in the Journal of Computational and Nonlinear Dynamic

Modelling of coupled cross-flow/in-line vortex-induced vibrations using double Duffing and van der Pol oscillators

Many studies have typically applied a linear structural spring–mass–damper oscillator and a van der Pol wake oscillator to model a one-dimensional cross-flow vortex-induced vibration (VIV). In this study, an advanced model for predicting a two-dimensional coupled cross-flow/in-line VIV of a flexibly mounted circular cylinder in a uniform flow is proposed and validated. The ensuing dynamical system is based on double Duffing–van der Pol (structural-wake) oscillators with the two structural equations containing both cubic and quadratic nonlinear terms. The cubic nonlinearities capture the geometrical coupling of cross-flow/in-line displacements excited by hydrodynamic lift/drag forces whereas the quadratic nonlinearities allow the wake–cylinder interactions. Some empirical coefficients are calibrated against published experimental results to establish a new generic analytical function accounting for the dependence of VIV on a physical mass and/or damping parameter. By varying flow velocities in the numerical simulations, the derived low-order model captures several important VIV characteristics including a two-dimensional lock-in, hysteresis phenomenon and figure-of-eight trajectory tracing the periodically coupled in-line/cross-flow oscillations with their tuned two-to-one resonant frequencies. By making use of a newly derived empirical formula, the predicted maximum cross-flow/in-line VIV amplitudes and associated lock-in ranges compare well with several experimental results for cylinders with low/high mass or damping ratios. Moreover, the parametric studies highlight the important effect of geometrical nonlinearities through new displacement coupling terms and the ratio of in-line to cross-flow natural frequencies of the freely vibrating cylinder

Nonlinear multi-mode interactions in subsea risers undergoing vortex-induced vibrations

This paper investigates nonlinear multi-mode interactions in subsea risers undergoing vortex-induced vibrations based on a computationally efficient reduced-order fluid-structure interaction model. Cross-flow responses as a result of a steady uniform current are considered. The geometrically nonlinear equations of riser motion are coupled with nonlinear wake oscillators which have been modified to capture the effect of initial curvatures of curved cylinder and to approximate the space-time varying hydrodynamic lift forces. The main objectives are to provide new insights into the vortex-induced vibration characteristics of risers under external and internal resonances and to distinguish nonlinear dynamic behaviors between curved catenary and straight toptensioned risers. The analyses of multi-mode contributions, lock-in regimes, response amplitudes, resonant nonlinear modes and curvatures are carried out and several interesting aspects are highlighted

Unconditional measurement-based quantum computation with optomechanical continuous variables

Universal quantum computation encoded over continuous variables can be achieved via Gaussian measurements acting on entangled non-Gaussian states. However, due to the weakness of available nonlinearities, generally these states can only be prepared conditionally, potentially with low probability. Here we show how universal quantum computation could be implemented unconditionally using an integrated platform able to sustain both linear and quadratic optomechanical-like interactions. Specifically, considering cavity opto- and electro-mechanical systems, we propose a realisation of a driven-dissipative dynamics that deterministically prepares the required non-Gaussian cluster states --- entangled squeezed states of multiple mechanical oscillators suitably interspersed with cubic-phase states. We next demonstrate how arbitrary Gaussian measurements on the cluster nodes can be performed by continuously monitoring the output cavity field. Finally, the feasibility requirements of this approach are analysed in detail, suggesting that its building blocks are within reach of current technology.Comment: 5 pages + 9 pages supplementary materia

Vortex-induced vibration of catenary riser: reduced-order modeling and lock-in analysis using wake oscillator

A new reduced-order model capable of analyzing the vortex-induced vibration of catenary riser in the ocean current has been developed. This semi analytical-numerical approach is versatile and allows for a significant reduction in computational effort for the analysis of fluid-riser interactions. The incoming current flow is assumed to be steady, uniform, unidirectional and perpendicular to the riser plane of initial equilibrium curvatures