Limit Cycle Flutter Analysis of Plate-Type Beam with Dissymmetrical Subsection Linear Stiffness

2011 ◽  
Vol 66-68 ◽  
pp. 1732-1737
Author(s):  
Li Lu ◽  
Yi Ren Yang ◽  
Chen Guang Fan ◽  
Ming Lu Zhang
Keyword(s):  
Galerkin Method ◽  
Viscous Flow ◽  
Limit Cycle ◽  
Equivalent Linearization ◽  
Incompressible Viscous Flow ◽  
Flutter Analysis ◽  
Limit Cycle Flutter ◽  
The Stability ◽  
Theoretical Results ◽  
Plate Type

The limit cycle flutter of a plate-type structure with dissymmetrical subsection linear stiffness in incompressible viscous flow was studied. Galerkin Method was used to get the differential equations of system. The equivalent linearization concept was performed to predict the ranges of limit cycle flutter velocities. The flutter borderline map was used to analyze the the stability of limit cycle flutter. By numerical integrating, the velocities of convergence, flutter and instability were obtained. The theoretical results agree well with the results of numerical integration.

Efficient Method for Limit Cycle Flutter Analysis Based on Nonlinear Aerodynamic Reduced-Order Models

AIAA Journal ◽  
2012 ◽  
Vol 50 (5) ◽  
pp. 1019-1028 ◽  
Author(s):  
Weiwei Zhang ◽  
Bobin Wang ◽  
Zhengyin Ye ◽  
Jingge Quan
Keyword(s):  
Limit Cycle ◽  
Efficient Method ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Flutter Analysis ◽  
Limit Cycle Flutter ◽  
Nonlinear Aerodynamic

On the stability of the space–time discontinuous Galerkin method for the numerical solution of nonstationary nonlinear convection–diffusion problems

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Monika Balázsová ◽  
Miloslav Feistauer ◽  
Martin Hadrava ◽  
Adam Kosík
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Space Time ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
The Subject ◽  
The Stability ◽  
Theoretical Results ◽  
Diffusion Problems

AbstractThe subject of this paper is the analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of the numerical scheme, the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion terms and interior and boundary penalty are used. Then error estimates are briefly characterized. The main attention is paid to the investigation of unconditional stability of the method. An important tool is the concept of the discrete characteristic function. Theoretical results are accompanied by numerical experiments.

Limit Cycle Flutter Analysis of a High-Aspect-Ratio Wing with an External Store

2014 ◽  
Vol 912-914 ◽  
pp. 907-910 ◽  
Author(s):  
Jun Xu ◽  
Xiao Ping Ma
Keyword(s):  
Aspect Ratio ◽  
Limit Cycle ◽  
High Aspect Ratio ◽  
Structural Model ◽  
Bifurcation Diagrams ◽  
Governing Equations ◽  
Time Simulation ◽  
Flutter Analysis ◽  
Structural Nonlinearities ◽  
Limit Cycle Flutter

Limit cycle flutter analysis of a high-aspect-ratiowing with an external store is presented. The concentrated store mass iscombined into the governing equations which are obtained using the extendedHamilton’s principle. The high-aspect-ratio wing structural model, which alsoconsiders the in-plane bending motion, is used. Three possible nonlinearitiesare considered including structural nonlinearities, aerodynamic nonlinearities,and store nonlinearities. Time simulation and bifurcation diagrams areperformed to analysis systems with three nonlinearities.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

Numerical methods for incompressible viscous flow

2002 ◽  
Vol 25 (8-12) ◽  
pp. 1125-1146 ◽  
Author(s):  
Hans Petter Langtangen ◽  
Kent-Andre Mardal ◽  
Ragnar Winther
Keyword(s):  
Numerical Methods ◽  
Viscous Flow ◽  
Incompressible Viscous Flow

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

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