General nonlinear analysis of second-order oscillators

2000 ◽  
Vol 36 (5) ◽  
pp. 396 ◽  
Author(s):  
A. Buonomo ◽  
A. Lo Schiavo
Keyword(s):  
Nonlinear Analysis ◽  
Second Order

A MATHEMATICAL MODEL OF ANEURYSM OF CIRCLE OF WILLIS

1995 ◽  
Vol 03 (03) ◽  
pp. 653-659 ◽  
Author(s):  
J. J. NIETO ◽  
A. TORRES
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Ordinary Differential Equation ◽  
Blood Flow ◽  
Nonlinear Analysis ◽  
Existence Of Solutions ◽  
Circle Of Willis ◽  
Second Order ◽  
Qualitative Properties

We introduce a new mathematical model of aneurysm of the circle of Willis. It is an ordinary differential equation of second order that regulates the velocity of blood flow inside the aneurysm. By using some recent methods of nonlinear analysis, we prove the existence of solutions with some qualitative properties that give information on the causes of rupture of the aneurysm.

scholarly journals Nonlinear Sum Operator Equations with a Parameter and Application to Second-Order Three-Point BVPs

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Wen-Xia Wang ◽  
Xi-Lan Liu ◽  
Piao-Piao Shi
Keyword(s):  
Nonlinear Analysis ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Critical Value ◽  
Second Order ◽  
Point Boundary ◽  
Operator Equations

A class of nonlinear sum operator equations with a parameter on order Banach spaces were considered. The existence and uniqueness of positive solutions for this kind of operator equations and the dependence of solutions on the parameter have been obtained by using the properties of cone and nonlinear analysis methods. The critical value of the parameter was estimated. Further, the application to some nonlinear three-point boundary value problems was given to show the significance of the discussion.

Estimation of Second-Order Effects for Pole-Type Structures

2000 ◽  
Vol 1740 (1) ◽  
pp. 151-156 ◽  
Author(s):  
Edgar Nunez ◽  
Fouad H. Fouad
Keyword(s):  
Nonlinear Analysis ◽  
Traffic Signals ◽  
Second Order ◽  
Order Effects ◽  
Simplified Approach ◽  
Bending Stresses ◽  
Pole Type ◽  
Second Order Effects ◽  
Factor C ◽  
Highway Signs

The design of pole-type structures for highway supports requires computation of second-order effects induced by the interaction of vertical gravitational and transverse wind loads. The 1994 Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals provides two methods to account for those second-order effects. The first method uses a simplified approach by introducing a factor, CA, into the combined stress ratio equation. The second method requires the computation of the exact bending stresses by means of a nonlinear analysis. Most structural design codes specify simplified methods for the evaluation of second-order effects to facilitate the design of structural members by using the forces obtained in a first-order static analysis. Therefore, simplified methods must be accurate to be considered an adequate alternative to a more sophisticated analysis. The purpose of this study was to determine the accuracy of the simplified method by using the CA factor to estimate the second-order effects for pole-type structures. An analytical study that included 241 pole configurations was conducted to evaluate the CA factor. Exact solutions were computed by using a computer program capable of performing second-order analysis. The study indicated that for typical pole-type structures, the results obtained with the CA factor were highly conservative. On the basis of the results, a modified expression for the CA factor is proposed. Results obtained by use of the modified expression for the CA factor were within 10 percent of those obtained by use of the “exact” nonlinear analysis.

Fault Distance Calculation in Radial Distribution System Using Second Order Polynomial Analysis of Voltage Sag Profile

2015 ◽  
Vol 785 ◽  
pp. 460-464
Author(s):  
S.S. Gururajapathy ◽  
Hazlie Mokhlis ◽  
Hazlee Azil Illias ◽  
Lilik Jamilatul Awalin
Keyword(s):  
Nonlinear Analysis ◽  
Distribution System ◽  
Second Order ◽  
Percentage Error ◽  
Voltage Sag ◽  
Test Results ◽  
Actual Distribution ◽  
Radial Distribution System ◽  
Distance Calculation ◽  
Order Polynomial

This paper proposes a nonlinear analysis of voltage sag magnitude and angle for fault distance calculation in distribution system. The method first identifies the fault section. Then, a rank approach is followed to identify and prioritize the faulty section. Later, the fault distance is calculated by creating a second order polynomial passing through the fault node. The testing is carried out in an actual distribution system of an electrical utility in Malaysia with 37 nodes. The test results show that the proposed fault distance gives very small percentage error.

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