Nonlinear Stability Analysis of Ship Towed by Elastic Rope

1986 ◽  
Vol 30 (02) ◽  
pp. 136-146 ◽  
Author(s):  
Michael M. Bernitsas ◽  
Nikos S. Kekridis
Keyword(s):  
Stability Analysis ◽  
Phase Space ◽  
Local Analysis ◽  
Nonlinear Stability Analysis ◽  
Independent System ◽  
Course Stability ◽  
Dependent Model ◽  
The Stability ◽  
Nonlinear Elastic ◽  
Time Dependent Model

The course stability of a towed vessel is traditionally assessed using local linear analysis of a time-independent system of a ship towed by an inelastic towline. In this work a method is developed for studying the global stability of a nonlinear time-dependent model of the horizontal plane motions of a ship towed by a nonlinear elastic rope. First, the critical points of the corresponding autonomous system are found in the phase space and their nature is determined by local analysis. Then the global behavior of the trajectories in the phase space is predicted on the basis of the local analysis results. The results of the stability analysis are verified by comparison with the solution of the model by simulation. A barge, a tanker and a Mariner, with markedly different course stability characteristics, towed by two different elastic ropes are used to illustrate the method.

A Nonlinear Stability Analysis for Difference Equations Using Semi-Implicit Mobility

1977 ◽  
Vol 17 (01) ◽  
pp. 79-91 ◽  
Author(s):  
D.W. Peaceman
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Finite Difference ◽  
Nonlinear Stability ◽  
Difference Equations ◽  
Nonlinear Stability Analysis ◽  
Time Step ◽  
Two Phase ◽  
Linearized Stability ◽  
The Stability

Abstract The usual linearized stability analysis of the finite-difference solution for two-phase flow in porous media is not delicate enough to distinguish porous media is not delicate enough to distinguish between the stability of equations using semi-implicit mobility and those using completely implicit mobility. A nonlinear stability analysis is developed and applied to finite-difference equations using an upstream mobility that is explicit, completely implicit, or semi-implicit. The nonlinear analysis yields a sufficient (though not necessary) condition for stability. The results for explicit and completely implicit mobilities agree with those obtained by the standard linearized analysis; in particular, use of completely implicit mobility particular, use of completely implicit mobility results in unconditional stability. For semi-implicit mobility, the analysis shows a mild restriction that generally will not be violated in practical reservoir simulations. Some numerical results that support the theoretical conclusions are presented. Introduction Early finite-difference, Multiphase reservoir simulators using explicit mobility were found to require exceedingly small time steps to solve certain types of problems, particularly coning and gas percolation. Both these problems are characterized percolation. Both these problems are characterized by regions of high flow velocity. Coats developed an ad hoc technique for dealing with gas percolation, but a more general and highly successful approach for dealing with high-velocity problems has been the use of implicit mobility. Blair and Weinaug developed a simulator using completely implicit mobility that greatly relaxed the time-step restriction. Their simulator involved iterative solution of nonlinear difference equations, which considerably increased the computational work per time step. Three more recent papers introduced the use of semi-implicit mobility, which proved to be greatly superior to the fully implicit method with respect to computational effort, ease of use, and maximum permissible time-step size. As a result, semi-implicit mobility has achieved wide use throughout the industry. However, this success has been pragmatic, with little or no theoretical work to justify its use. In this paper, we attempt to place the use of semi-implicit mobility on a sounder theoretical foundation by examining the stability of semi-implicit difference equations. The usual linearized stability analysis is not delicate enough to distinguish between the semi-implicit and completely implicit difference equation. A nonlinear stability analysis is developed that permits the detection of some differences between the stability of difference equations using implicit mobility and those using semi-implicit mobility. DIFFERENTIAL EQUATIONS The ideas to be developed may be adequately presented using the following simplified system: presented using the following simplified system: horizontal, one-dimensional, two-phase, incompressible flow in homogeneous porous media, with zero capillary pressure. A variable cross-section is included so that a variable flow velocity may be considered. The basic differential equations are (1) (2) The total volumetric flow rate is given by (3) Addition of Eqs. 1 and 2 yields =O SPEJ P. 79

Nonlinear Stability Analysis of Thin-Walled Pier

2013 ◽  
Vol 361-363 ◽  
pp. 1251-1254
Author(s):  
Xiao Mei Dong
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Shell Element ◽  
Nonlinear Stability Analysis ◽  
Nonlinearity Effect ◽  
Updated Lagrangian Formulation ◽  
Thin Walled ◽  
Displacement Theory ◽  
The Stability ◽  
Updated Lagrangian

Shell element was used to simulate thin-walled piers. Mander constitutive model was adopted for analysis about the material nonlinearity. By finite displacement theory the geometric nonlinearity effect was reckoned in stability analysis based on Updated Lagrangian formulation. Nonlinear stability analysis during different construction stages indicates that the stability of pier in cantilever stage is weakest. Considered the dual non-linearity, the stability coefficient descends distinctly.

Leakage Current Based Thermal Modeling of Glass Disc Insulator Surface

2017 ◽  
Vol 6 (3) ◽  
pp. 504
Author(s):  
Mohammed Imran Mousa ◽  
Zulkurnain Abdul-Malek ◽  
Zainab Imran Mousa
Keyword(s):  
Transmission Lines ◽  
Comsol Multiphysics ◽  
Insulator Surface ◽  
Glass Disc ◽  
Element Simulation ◽  
Glass Insulation ◽  
Glass Insulator ◽  
Dependent Model ◽  
The Stability ◽  
Time Dependent Model

The stability of transmission lines relies on the health of the insulators, such as glass string insulators, which may occasionally flashover during an overvoltage. The likelihood of flashover increases notably when the glass insulator is wrapped by a wet contaminant layer. In this paper a study of the surface thermal profile of glass disc insulators insulation had been carried out for both clean and polluted surfaces. A finite-element simulation with time dependent model was carried out using COMSOL Multiphysics software. The variation of the insulator surface temperature with applied voltage as well as with pollution layer thickness is explained. The results illustrate the significant effect of pollution conductivity on heat propagate along the surface of the glass insulators with the increase higher voltages' magnitudes. Study of the aging level impact on a steady state thermal for glass insulation surface is also carried out.

Burgers and mKdV equation for car-following model considering drivers’ characteristics on a gradient highway

2018 ◽  
Vol 32 (26) ◽  
pp. 1850314 ◽  
Author(s):  
Di-Hua Sun ◽  
Peng Tan ◽  
Dong Chen ◽  
Fei Xie ◽  
Lin-Hui Guan
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Burgers Equation ◽  
Mkdv Equation ◽  
Nonlinear Stability Analysis ◽  
Car Following ◽  
Jamming Transition ◽  
The Road ◽  
Car Following Model ◽  
The Stability

In this paper, we propose a new car-following model considering driver’s timid and aggressive characteristics on a gradient highway. Based on the control theory, the linear stability analysis of the model was conducted. It shows that the stability of traffic flow on the gradient highway varies with the drivers’ characteristics and the slope. Adopting nonlinear stability analysis, the Burgers equation and modified Korteweg–de Vries (mKdV) equation are derived to describe the triangular shock waves and kink–antikink waves, respectively. The theoretical and numerical results show that aggressive drivers tend to stabilize traffic flow but timid drivers tend to destabilize traffic flow on a gradient highway both on an uphill situation and on a downhill situation. Moreover, the slope of the road also plays an important role in traffic jamming transition.

Instability Analysis of High Pier of Continuous Rigid Frame Bridges

2012 ◽  
Vol 178-181 ◽  
pp. 1989-1993
Author(s):  
Xiao Mei Dong
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Geometric Nonlinearity ◽  
Material Nonlinearity ◽  
Thin Wall ◽  
Nonlinear Stability Analysis ◽  
Stability Coefficient ◽  
Rigid Frame ◽  
High Pier ◽  
The Stability

The linear and nonlinear stability of continuous rigid frame bridge with thin-wall piers is analyzed by using the current FEM software. Linear stability analysis indicates that coefficient of stability in cantilever stage is poorest. Two aspects are included in nonlinear stability analysis. The first one, only geometric nonlinearity is considered and the other one, geometric nonlinearity and material nonlinearity are considered simultaneously. The results show that material nonlinearity is a factor to stability coefficient that can not be overlooked. Considered the dual non-linearity, the stability coefficient descends consumedly.

scholarly journals The influence of front strength on the development and equilibration of symmetric instability. Part 1. Growth and saturation

2021 ◽  
Vol 926 ◽  
Author(s):  
A.F. Wienkers ◽  
L.N. Thomas ◽  
J.R. Taylor
Keyword(s):  
Stability Analysis ◽  
Shear Instability ◽  
Nonlinear Stability Analysis ◽  
Coriolis Parameter ◽  
Weakly Nonlinear ◽  
Thermal Wind ◽  
Inertial Instability ◽  
Slantwise Convection ◽  
The Stability ◽  
Symmetric Instability

Submesoscale fronts with large horizontal buoyancy gradients and $O(1)$ Rossby numbers are common in the upper ocean. These fronts are associated with large vertical transport and are hotspots for biological activity. Submesoscale fronts are susceptible to symmetric instability (SI) – a form of stratified inertial instability which can occur when the potential vorticity is of the opposite sign to the Coriolis parameter. Here, we use a weakly nonlinear stability analysis to study SI in an idealised frontal zone with a uniform horizontal buoyancy gradient in thermal wind balance. We find that the structure and energetics of SI strongly depend on the front strength, defined as the ratio of the horizontal buoyancy gradient to the square of the Coriolis frequency. Vertically bounded non-hydrostatic SI modes can grow by extracting potential or kinetic energy from the balanced front and the relative importance of these energy reservoirs depends on the front strength and vertical stratification. We describe two limiting behaviours as ‘slantwise convection’ and ‘slantwise inertial instability’ where the largest energy source is the buoyancy flux and geostrophic shear production, respectively. The growing linear SI modes eventually break down through a secondary shear instability, and in the process transport considerable geostrophic momentum. The resulting breakdown of thermal wind balance generates vertically sheared inertial oscillations and we estimate the amplitude of these oscillations from the stability analysis. We finally discuss broader implications of these results in the context of current parameterisations of SI.

Stability Analysis of Nantong Sports and Exhibition Center Based on Measured Geometrical Imperfections

2010 ◽  
Vol 163-167 ◽  
pp. 426-432
Author(s):  
Cai Qi Zhao ◽  
Jun Ma ◽  
De Lin Li
Keyword(s):  
Stability Analysis ◽  
Statistical Parameter ◽  
Test Method ◽  
Nonlinear Stability Analysis ◽  
Initial Shape ◽  
Long Span ◽  
Geometrical Imperfection ◽  
Geometrical Imperfections ◽  
The Stability ◽  
Stochastic Distribution

Position deviation of joints is a primary initial geometrical imperfection that affects the stability of long-span spatial structures. It makes field measurement of joint coordinate for the shell and roof initial shape of Nantong Sports Exhibition Center upon its completion. This paper researches the stochastic distribution feature and statistical parameter of geometrical imperfections for the data sources of above position deviation of joints by “abnormal data test method”. The results indicate that the distribution of abnormal data is concentrated, which is related to the difficulty of construction and condition of measurement; the distribution of joint position deviation can be assumed by normal distribution, and its mean μ=0 and mean square deviation σ=R/2 of statistical parameter are tenable. Meanwhile, It also puts forward a stochastic imperfection method based on measured imperfections and ANSYS－PDS platform, establishes a measured model to make nonlinear stability analysis, and respectively compares this critical load with that obtained by the perfect structure of ideal shape and the consistent imperfection method, so as to evaluate the stability and reliability of practical project in an objective manner, and provide reference for project design.

Maneuvering Model for FPSOs and Stability Analysis of the Offloading Operation

2002 ◽  
Vol 124 (4) ◽  
pp. 196-202 ◽  
Author(s):  
Sergio H. Sphaier ◽  
Antonio C. Fernandes ◽  
Sylvio H. S. Correa ◽  
Gustavo A. V. Castro
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Classical Theory ◽  
Deep Water ◽  
Experimental Test ◽  
Dynamic Systems ◽  
Scale Effects ◽  
Local Analysis ◽  
Floating System ◽  
The Stability

The discovery of new fields in deep water brought back the use of large ships such as FPSOs. This seems to be the trend toward ultra deep water units at least in offshore Brazil. At about the same time, VLCCs (very large crude carriers) have been converted to work as FPSOs. However, working as a stationary unit a VLCC presents directional stability problems. In the present paper a methodology is discussed to develop a mathematical model for the simulation and the verification of the stability of a VLCC working as a FPSO. To express the forces and moments acting on the ship hull the results of a group of experiments are described in the classical sense of the maneuverability theory, although they concern large angles of attack and low advance velocity. Besides, a procedure to determine the stability of the floating system is also presented. This is based on local analysis and follows the classical theory of dynamic systems. Further, the use of stabilization devices for a floating unit and the offloading operation are discussed. Finally, an experimental test is proposed, in order to take into account scale effects.

Linear and Nonlinear Stability Analysis of a Supercritical Natural Circulation Loop

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Manish Sharma ◽  
P. K. Vijayan ◽  
D. S. Pilkhwal ◽  
D. Saha ◽  
R. K. Sinha
Keyword(s):  
Stability Analysis ◽  
Supercritical Water ◽  
Natural Circulation ◽  
Computer Code ◽  
Circulation Loop ◽  
Nonlinear Stability Analysis ◽  
Stability Behavior ◽  
Natural Circulation Loop ◽  
Linear And Nonlinear ◽  
The Stability

Supercritical water (SCW) has excellent heat transfer characteristics as a coolant for nuclear reactors. Besides it results in high thermal efficiency of the plant. However, the flow can experience instabilities in supercritical water cooled reactors, as the density change is very large for the supercritical fluids. A computer code SUCLIN has been developed employing supercritical water properties to carry out the steady-state and linear stability analysis of a SCW natural circulation loop (SCWNCL). The conservation equations of mass, momentum, and energy have been linearized by imposing small perturbation in flow rate, enthalpy, pressure, and specific volume. The equations have been solved analytically to generate the characteristic equation. The roots of the equation determine the stability of the system. The code has been benchmarked against published results. Then the code has been extensively used for studying the effect of diameter, heater inlet temperature, and pressure on steady-state and stability behavior of a SCWNCL. A separate computer code, NOLSTA, has been developed, which investigates stability characteristics of supercritical natural circulation loop using nonlinear analysis. The conservation equations of mass, momentum, and energy in transient form were solved numerically using finite volume method. The stable, unstable, and neutrally stable points were identified by examining the amplitude of flow and temperature oscillations with time for a given set of operating conditions. The stability behavior of loop, predicted using nonlinear analysis has been compared with that obtained from linear analysis. The results show that the stability maps obtained by the two methods agree qualitatively. The present paper describes the linear and nonlinear stability analysis models and the results obtained in detail.

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