Generalized Adaptive Backstepping Synchronization for Non-Identical Parametrically Excited Systems

In this paper, we investigate the synchronization of chaotic systems consisting of non-identical parametrically excited oscillators. The backstepping design, which is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller is generalized and employed so as to achieve global chaos synchronization between a parametrically excited gyroscope and each of the parametrically excited pendulum and Duffing oscillator. Numerical simulations are implemented to verify the results

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

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

DYNAMICS OF AN UMBILICAL CABLE FOR UNDERGROUND BORE-WELL APPLICATIONS

A general model for an umbilical cable for underground bore-well applications is considered. The response of one-degree-of-freedom, nonlinear system under external excitation forces and the effect of the parameters 2, β and f on the excited system are investigated. Variation of the parameter 2 leads to multi-valued amplitudes and hence to jump phenomena. The simulation results are achieved using MATLAB 7.12.0 (R2011a) Simulink

Fast-slow analysis for parametrically and externally excited systems with two slow rationally related excitation frequencies

ACKNOWLEDGMENTS The authors express their gratitude to the anonymous reviewers for their valuable comments and suggestions that help to improve the paper. This work was supported by the National Natural Science Foundation of China (Grants No. 11202085, No. 21276115, No. 11302087, No. 11302086, and No. 11402226), the Natural Science Foundation of Jiangsu Province (Grant No. BK20130479), and the Research Foundation for Advanced Talents of Jiangsu University (Grant No. 11JDG075 ).Peer reviewe

The dynamics of the pendulum suspended on the forced Duffing oscillator

We investigate the dynamics of the pendulum suspended on the forced Duffing oscillator. The detailed bifurcation analysis in two parameter space (amplitude and frequency of excitation) which presents both oscillating and rotating periodic solutions of the pendulum has been performed. We identify the areas with low number of coexisting attractors in the parameter space as the coexistence of different attractors has a significant impact on the practical usage of the proposed system as a tuned mass absorber.Comment: Accepte

New model for vortex-induced vibration of catenary riser

This paper presents a new theoretical model capable of predicting the vortex-induced vibration response of a steel catenary riser subject to a steady uniform current. The equations governing riser in-plane/out-ofplane (cross-flow/in-line) motion are based on a pinned beam-cable model accounting for overall effects of bending, extensibility, sag, inclination and structural nonlinearities. The empirically hydrodynamic model is based on nonlinear wake oscillators describing the fluctuating lift/drag forces. Depending on the potentially vortex-induced modes and system parameters, a reduced-order fluid-structure interaction model is derived which entails a significantly reduced computational time effort. Parametric results reveal maximum response amplitudes of risers, along with the occurrence of uni-modal lock-in phenomenon

​ Time Delay Control and Frequency Splitting in the forced Kadomtsev-Petviashvili Equation ​

A time delay control is applied to the forced Kadomtsev-Petviashvili (KP) equation Using an appropriate perturbation method, we derive nonlinear equations describing amplitude and phase of the response anfd discuss in some detail external force-response and frequency-response curves for the fundamental resonance. For the uncontrolled system, we find a frequency splitting, a second frequency aappears in addition to the forcing one. Saddle-center bifurcation, jumps and hysteresis phenomena are observed together with closed orbits of the slow flow equations. There are stable two-period quasi-periodic modulated motion for the KP equation with amplitudes depending on the initial conditions . Subsequently, we study the controlled system finding sufficient conditions for a periodic behavior. We can accomplish a successful control because the amplitude peak of the fundamental resonance can be reduced and the saddle-center bifurcations and two-period quasi-periodic motions can be removed by adequate choices for delay and feedback gains