Hydrodynamic Memory Effect on Stability, Bifurcation, and Chaos of Two-Point Mooring Systems

1997 ◽  
Vol 41 (01) ◽  
pp. 26-44
Author(s):  
Jin-Sug Chung ◽  
Michael M. Bernitsas
Keyword(s):  
Memory Effect ◽  
Design Parameters ◽  
Wave Loads ◽  
Mooring Lines ◽  
Stability Boundaries ◽  
The Stability ◽  
Systems With Memory ◽  
Hydrodynamic Wave ◽  
Nonlinear Elastic ◽  
With Memory

The stability properties of two-point mooring systems governed by their slow horizontal motions are studied theoretically. The often-neglected memory effect due to hydrodynamic wave loads change—in some cases critically—the stability boundaries in the system design space. The third-order maneuvering equations and a nonlinear elastic spring model are used to describe the dynamics of the moored vessel and the mooring lines, respectively. The resulting model accurately represents a two-point mooring system and can be used for stability analysis in the sense of Lyapunov. The stability charts of mooring systems with memory effects exhibit considerable differences from systems without memory in local regions of bifurcation diagrams. Further, the pattern of these changes of stability boundaries varies with the hydrodynamic properties of the moored vessel and/or the environmental conditions. The findings of this study suggest that the number of influencing design parameters can be much more than the present stability theory of dynamical systems can handle. They prove, however, that neglecting the memory effect may result in selecting unsafe configurations of two-point mooring systems.

Turret Mooring Design Based on Analytical Expressions of Catastrophes of Slow-Motion Dynamics

1998 ◽  
Vol 120 (3) ◽  
pp. 154-164 ◽  
Author(s):  
M. M. Bernitsas ◽  
L. O. Garza-Rios
Keyword(s):  
Parametric Design ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Slow Motion ◽  
Sensitivity Analyses ◽  
Design Parameters ◽  
Mooring Lines ◽  
The Stability ◽  
Fifth Order ◽  
Analytical Expressions

Analytical expressions of the bifurcation boundaries exhibited by turret mooring systems (TMS), and expressions that define the morphogeneses occurring across boundaries are developed. These expressions provide the necessary means for evaluating the stability of a TMS around an equilibrium position, and constructing catastrophe sets in two or three-dimensional parametric design spaces. Sensitivity analyses of the bifurcation boundaries define the effect of any parameter or group of parameters on the dynamical behavior of the system. These expressions allow the designer to select appropriate values for TMS design parameters without resorting to trial and error. A four-line TMS is used to demonstrate this design methodology. The mathematical model consists of the nonlinear, fifth-order, low-speed, large-drift maneuvering equations. Mooring lines are modeled with submerged catenaries, and include nonlinear drag. External excitation consists of time-independent current, wind, and mean wave drift.

STABILITY OF STOCHASTIC SYSTEMS WITH MEMORY

2005 ◽  
Vol 05 (02) ◽  
pp. 223-232 ◽  
Author(s):  
V. D. POTAPOV
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Stochastic Systems ◽  
Wide Band ◽  
Statistical Simulation ◽  
Statistical Moments ◽  
Fading Memory ◽  
The Stability ◽  
Systems With Memory ◽  
With Memory

Many processes in physics, biology, ecology, mechanics etc. can be modeled by Volterra integro-differential equations (VIDEs) with "fading memory". Often the behaviour of corresponding systems is perturbed by random noises. One of the main problems for the theory of stochastic Volterra integro-differential equations (SVIDEs) is connected with their stability. The present paper is devoted to the numerical solution of the stability problem for linear SVIDEs. The method is based on the statistical simulation of input random wide-band stationary processes, which are assumed in the form of "colored" noises. For each realization the numerical solution of VIDEs is found. The conclusion about the stability of the considered system SVIDE with respect to statistical moments is made on the basis of Liapunov exponents, which are calculated for statistical moments of the solution.

Automated Stability Analysis of a Vehicle in Combined Pitch and Roll

2002 ◽  
Author(s):  
James K. Sprague ◽  
Shyi-Ping Liu
Keyword(s):  
Stability Analysis ◽  
Rigid Body ◽  
Contact Forces ◽  
Design Parameters ◽  
Spherical Coordinates ◽  
Stability Boundaries ◽  
Overturning Stability ◽  
Heading Angle ◽  
The Stability ◽  
Six Degree Of Freedom

This paper presents a rigid body modeling approach using ADAMS™ for an overturning stability analysis of a vehicle stopped at an arbitrary heading angle on a steep grade. The vehicle is modeled as a six-degree-of-freedom rigid body with multiple contact forces acting on the ground. A gravity vector bounded by sets of spherical coordinates is applied to the vehicle to represent the physics of a vehicle stopped on a grade with any arbitrary combination of pitch and roll angles. A design of experiments study is performed to locate the overturning stability boundaries within given levels of design parameters. Results are output using two effective graphical means of depicting the stability regions and magnitude of contact forces.

scholarly journals The Memory Effect on Fractional Calculus: An Application in the Spread of Covid-19

2020 ◽  
Author(s):  
Laécio Carvalho de Barros ◽  
Michele Martins Lopes ◽  
Francielle Santo Pedro Simões ◽  
Estevão Esmi ◽  
José Paulo Carvalho dos Santos ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Fractional Calculus ◽  
Memory Effect ◽  
Compartmental Model ◽  
Statistical Approach ◽  
Hysteresis Phenomenon ◽  
Fractional Operators ◽  
Main Interest ◽  
Systems With Memory ◽  
With Memory

Abstract Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest of this work is, through a statistical approach, to attest how the hysteresis phenomenon, which describes the memory effect present in biological systems, can be treated by fractional calculus, and to analyze the contribution of the historical values of a function in the evaluation of fractional operators according their order. In order to illustrate the efficiency of this non-integer order calculus, we consider the SIR (Susceptible-Infected-Recovered) compartmental model which is widely used in epidemiology. We employ SIR models to model the dynamics, with and without memory, of the spread of Covid-19 in some countries.

Dynamic Behaviour and Stability Analysis of Multibody Haptic Systems

2012 ◽  
Author(s):  
Sara Shayan-Amin ◽  
László L. Kovács ◽  
József Kövecses
Keyword(s):  
Dynamic Model ◽  
Force Feedback ◽  
Joint Model ◽  
Simplified Model ◽  
Design Parameters ◽  
Experimental Investigations ◽  
Stability Boundaries ◽  
Flexible Joint ◽  
Haptic Devices ◽  
The Stability

To investigate the effects of mechanical design parameters on the performance of force feedback haptic devices, a representative dynamic model of the system is required. In this paper, the experimental investigations conducted on a 2DoF haptic device revealed that flexibility associated with the joints reduced the stable domain of operation considerably. Therefore, dynamic model of the investigated mechanism including the joint flexibility and physical damping is considered. The stability boundaries achieved by using the proposed flexible joint model is in good agreement with experimental results. A simplified model of the system is then developed employing a decomposition proposed in [1]. It is shown that the stability limits obtained by this simplified model give a slightly conservative but close estimate to the stability boundaries of the higher DoF flexible joint model. Such a simplified and experimentally validated model can be used for impedance-type haptic devices. The developed model makes it possible to investigate the effect of different mechanical parameters on the performance of multibody haptic systems.

Dynamic Game and Pricing for Data Sponsored 5G Systems With Memory Effect

2020 ◽  
Vol 38 (4) ◽  
pp. 750-765 ◽  
Author(s):  
Shaohan Feng ◽  
Dusit Niyato ◽  
Xiao Lu ◽  
Ping Wang ◽  
Dong In Kim
Keyword(s):  
Memory Effect ◽  
Dynamic Game ◽  
5G Systems ◽  
Systems With Memory ◽  
With Memory

scholarly journals The Memory Effect on Fractional Calculus: An Application in the Spread of Covid-19

2021 ◽  
Author(s):  
Laécio Carvalho de Barros ◽  
Michele Martins Lopes ◽  
Francielle Santo Pedro Simões ◽  
Estevão Esmi ◽  
José Paulo Carvalho dos Santos ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Fractional Calculus ◽  
Memory Effect ◽  
Compartmental Model ◽  
Statistical Approach ◽  
Hysteresis Phenomenon ◽  
Fractional Operators ◽  
Main Interest ◽  
Systems With Memory ◽  
With Memory

Abstract Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest of this work is to attest, through a statistical approach, how the hysteresis phenomenon, which describes a type of memory effect present in biological systems, can be treated by fractional calculus. We also analyse the contribution of the historical values of a function in the evaluation of fractional operators according to their order. In order to illustrate the efficiency of this non-integer order calculus, we consider the SIR (Susceptible-Infected-Recovered) compartmental model which is widely used in epidemiology. We employ this compartmental model to study the dynamics of the spread of Covid-19 in some countries, one version with memory and one without memory.

scholarly journals A Method for Parametric Analysis of Stability Boundaries for Nonlinear Periodic Vibrations of Structures With Contact Interfaces

2018 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Parametric Analysis ◽  
Large Scale ◽  
Contact Stiffness ◽  
Stability Loss ◽  
Forced Response ◽  
Scale Model ◽  
Design Parameters ◽  
Stability Boundaries ◽  
Analysis Of Stability ◽  
The Stability

A method for parametric analysis of the stability loss boundary has been developed for periodic regimes of nonlinear forced vibrations for a first time. The method allows parametric frequency-domain calculations of the stability loss together with the vibration amplitudes and design parameter values corresponding to the stability boundaries. The tracing algorithm is applied to obtain the trajectories of stability loss points as functions of design parameters. The parametric stability loss is formulated for cases when: (i) the design parameters characterise the properties of nonlinear contact interfaces (e.g. gap, contact stiffness, friction coefficient, etc.) and (ii) the design parameters describe linear components of the analysed structure (e.g. parameters of geometric shape, material, natural frequencies, modal damping etc.) and (iii) these parameters describe the excitation loads (e.g. their level, distribution or frequency). An approach allowing the multiparametric analysis of stability boundaries is proposed. The method uses the multiharmonic representation of the periodic forced response and aimed at the analysis of realistic gas-turbine structures comprising thousands and millions degrees of freedom. The method can be used for the effective search of isolated branches of the nonlinear solutions and examples of detection and search of the isolated branches are given: for relatively small and for large-scale finite element models. The efficiency of the method for calculation of the stability boundaries and for the search of isolated branches is demonstrated on simple systems and on a large-scale model of a turbine blade.

scholarly journals A Method for Parametric Analysis of Stability Boundaries for Nonlinear Periodic Vibrations of Structures With Contact Interfaces

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Parametric Analysis ◽  
Large Scale ◽  
Contact Stiffness ◽  
Stability Loss ◽  
Forced Response ◽  
Scale Model ◽  
Design Parameters ◽  
Stability Boundaries ◽  
Analysis Of Stability ◽  
The Stability

A method for parametric analysis of the stability loss boundary has been developed for periodic regimes of nonlinear forced vibrations for a first time. The method allows parametric frequency-domain calculations of the stability loss together with the vibration amplitudes and design parameter values corresponding to the stability boundaries. The tracing algorithm is applied to obtain the trajectories of stability loss points as functions of design parameters. The parametric stability loss is formulated for cases when (i) the design parameters characterize the properties of nonlinear contact interfaces (e.g., gap, contact stiffness, and friction coefficient); (ii) the design parameters describe linear components of the analyzed structure (e.g., parameters of geometric shape, material, natural frequencies, and modal damping); and (iii) these parameters describe the excitation loads (e.g., their level, distribution or frequency). An approach allowing the multiparametric analysis of stability boundaries is proposed. The method uses the multiharmonic representation of the periodic forced response and aimed at the analysis of realistic gas-turbine structures comprising thousands and millions degrees-of-freedom (DOF). The method can be used for the effective search of isolated branches of the nonlinear solutions and examples of detection and search of the isolated branches are given: for relatively small and for large-scale finite element (FE) models. The efficiency of the method for calculation of the stability boundaries and for the search of isolated branches is demonstrated on simple systems and on a large-scale model of a turbine blade.

scholarly journals Analysis of the spread of COVID-19 in Morocco based on a SEIR epidemic model

2021 ◽  
Vol 10 (2) ◽  
pp. 72-78
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Mostafa Tahiri
Keyword(s):  
Mathematical Modeling ◽  
Fractional Calculus ◽  
Memory Effect ◽  
Epidemic Model ◽  
Evolutionary Systems ◽  
Integer Order ◽  
Systems With Memory ◽  
With Memory

Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. In order to illustrate the efficiency of this non-integer order calculus, we employ SEIR models to model the dynamics, with and without memory, of the spread of Covid-19 in Morocco country.

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