Advances in Computational Stability Analysis of Composite Aerospace Structures

2010 ◽  
Author(s):  
R. Degenhardt ◽  
F. C. de Araújo ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Stability Analysis ◽  
Computational Stability ◽  
Aerospace Structures

scholarly journals Computational Stability Analysis of Lotka-Volterra Systems

2016 ◽  
Vol 44 (2) ◽  
pp. 113-120
Author(s):  
Péter Polcz ◽  
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Stability Region ◽  
Stable Equilibrium ◽  
Linear Matrix ◽  
Stable Equilibrium Point ◽  
Computational Stability ◽  
Volterra Systems ◽  
Selection For ◽  
The Stability

Abstract This paper concerns the computational stability analysis of locally stable Lotka-Volterra (LV) systems by searching for appropriate Lyapunov functions in a general quadratic form composed of higher order monomial terms. The Lyapunov conditions are ensured through the solution of linear matrix inequalities. The stability region is estimated by determining the level set of the Lyapunov function within a suitable convex domain. The paper includes interesting computational results and discussion on the stability regions of higher (3,4) dimensional LV models as well as on the monomial selection for constructing the Lyapunov functions. Finally, the stability region is estimated of an uncertain 2D LV system with an uncertain interior locally stable equilibrium point.

scholarly journals Computational Stability Analysis of Diffusion‐Deformation Processes at Finite Strains

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Siddharth Sriram ◽  
Elten Polukhov ◽  
Marc-André Keip
Keyword(s):  
Stability Analysis ◽  
Finite Strains ◽  
Computational Stability ◽  
Deformation Processes

A Stability Analysis of Divergence Damping on a Latitude–Longitude Grid

2011 ◽  
Vol 139 (9) ◽  
pp. 2976-2993 ◽  
Author(s):  
Jared P. Whitehead ◽  
Christiane Jablonowski ◽  
Richard B. Rood ◽  
Peter H. Lauritzen
Keyword(s):  
Stability Analysis ◽  
General Circulation ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Circulation Model ◽  
Small Scale ◽  
Test Case ◽  
Baroclinic Wave ◽  
Computational Stability ◽  
Dynamical Core

The dynamical core of an atmospheric general circulation model is engineered to satisfy a delicate balance between numerical stability, computational cost, and an accurate representation of the equations of motion. It generally contains either explicitly added or inherent numerical diffusion mechanisms to control the buildup of energy or enstrophy at the smallest scales. The diffusion fosters computational stability and is sometimes also viewed as a substitute for unresolved subgrid-scale processes. A particular form of explicitly added diffusion is horizontal divergence damping. In this paper a von Neumann stability analysis of horizontal divergence damping on a latitude–longitude grid is performed. Stability restrictions are derived for the damping coefficients of both second- and fourth-order divergence damping. The accuracy of the theoretical analysis is verified through the use of idealized dynamical core test cases that include the simulation of gravity waves and a baroclinic wave. The tests are applied to the finite-volume dynamical core of NCAR’s Community Atmosphere Model version 5 (CAM5). Investigation of the amplification factor for the divergence damping mechanisms explains how small-scale meridional waves found in a baroclinic wave test case are not eliminated by the damping.

Computational Stability Analysis of Chatter in Turning

1997 ◽  
Vol 119 (4A) ◽  
pp. 457-460 ◽  
Author(s):  
S.-G. Chen ◽  
A. G. Ulsoy ◽  
Y. Koren
Keyword(s):  
Stability Analysis ◽  
Machine Tool ◽  
Characteristic Equation ◽  
Linear Time ◽  
Stability Index ◽  
Algebraic Equations ◽  
Machining Processes ◽  
Computational Stability ◽  
Linear Time Invariant ◽  
Excited Vibration

Machine tool chatter is one of the major constraints that limits productivity of the turning process. It is a self-excited vibration that is mainly caused by the interaction between the machine-tool/workpiece structure and the cutting process dynamics. This work introduces a general method which avoids lengthy algebraic (symbolic) manipulations in deriving, a characteristic equation. The solution scheme is simple and robust since the characteristic equation is numerically formulated as a single variable equation whose variable is well bounded rather than two nonlinear algebraic equations with unbounded variables. An asymptotic stability index is also introduced for a relative stability analysis. The method can be applied to other machining processes, as long as the system equations can be expressed as a set of linear time invariant difference-differential equations.

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