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Establishing a framework for the effective design of resilient supply chains with inherent non-linearities
Purpose of this paper: Previous control theory research on supply chain dynamics has predominantly taken a linear perspective of the real world, whereas nonlinearities have usually been studied via a simulation approach. Nonlinearities can naturally occur in supply chains through the existence of physical and economic constraints, for example, capacity limitations. Since the ability to flex capacity is an important aspect of supply chain resilience, there is a need to rigorously study such nonlinearities. Hence, the purpose of this paper is to propose a framework for the dynamic design of supply chains so that they are resilient to nonlinear system structures
Reduced-order modelling of vortex-induced vibration of catenary riser
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. The equations of riser 3-D motion are based on a pinned-pinned, tensioned-beam or flexural cable, modelling which accounts for overall effects of riser bending, extensibility, sag, inclination and structural nonlinearities. The unsteady hydrodynamic forces associated with cross-flow and in-line vibrations are modelled as distributed van der Pol wake oscillators. This hydrodynamic model has been modified in order to capture the effect of varying initial curvatures of the inclined flexible cylinder and to describe the space-time fluctuation of lift and drag forces. Depending on the vortex-excited in-plane/out-of-plane modes and system fluid-structure parameters, the parametric studies are carried out to determine the maximum response amplitudes of catenary risers, along with the occurrence of uni-modal lock-in phenomenon. The obtained results highlight the effect of initial curvatures and geometric nonlinearities on the nonlinear dynamics of riser undergoing vortex-induced vibration
Convective Nonlinearity in Non-Newtonian Fluids
In the limit of infinite yield time for stresses, the hydrodynamic equations
for viscoelastic, Non-Newtonian liquids such as polymer melts must reduce to
that for solids. This piece of information suffices to uniquely determine the
nonlinear convective derivative, an ongoing point of contention in the rheology
literature.Comment: 4 page
On the Systematic Constructions of Rotation Symmetric Bent Functions with Any Possible Algebraic Degrees
In the literature, few constructions of -variable rotation symmetric bent
functions have been presented, which either have restriction on or have
algebraic degree no more than . In this paper, for any even integer
, a first systemic construction of -variable rotation symmetric
bent functions, with any possible algebraic degrees ranging from to , is
proposed
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
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