Deterministic Stability Analysis of a Wind Loaded Structure

1978 ◽  
Vol 45 (1) ◽  
pp. 165-169 ◽  
Author(s):  
P. J. Holmes ◽  
Y. K. Lin
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Wind Loading ◽  
Qualitative Behavior ◽  
Stability Boundaries ◽  
Quantitative Estimates ◽  
Loading Problem ◽  
Loaded Structure ◽  
Excitation Conditions

We discuss the qualitative behavior of a pair of nonlinear differential equations arising in the study of a wind loading problem when turbulence terms are ignored. We obtain quantitative estimates of stability boundaries and are able to identify the most dangerous excitation conditions. This deterministic study provides the basis for further work on the full stochastic differential equations resulting when turbulence terms are included.

scholarly journals Behavior of second order nonlinear differantial equations

1978 ◽  
Vol 1 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Rina Ling
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Qualitative Behavior

Qualitative behavior of second order nonlinear differential equations with variable coefficients is studied. It includes properties such as positivity, number of zeroes, oscillatory behavior, boundedness and monotonicity of the solutions.

scholarly journals Stability Analysis and Numerical Solutions of a Competition Model with the Effects of Distribution Parameters

2019 ◽  
Vol 43 (1) ◽  
pp. 95-106
Author(s):  
Md Kamrujjaman ◽  
Sadia Akter Lima ◽  
Sonia Akter ◽  
Tanzila Eva
Keyword(s):  
Mathematical Biology ◽  
Stability Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Population Models ◽  
Distribution Parameters ◽  
Academy Of Sciences ◽  
Linearization Techniques

A system of two nonlinear differential equations in mathematical biology is considered. These models are originally stimulated by population models in biology when solutions are required to be non-negative, but the ordinary differential equations can be understood outside of this conventional scope of population models. The focus of this paper is on the use of linearization techniques, and Hartman Grobman theory to analyze nonlinear differential equations. We provide stability analysis and numerical solutions for these models that describe behaviors of solutions based only on the parameters used in the formulation of the systems. Journal of Bangladesh Academy of Sciences, Vol. 43, No. 1, 95-106, 2019

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