COMPLEX NORMAL FORM FOR STRONGLY NON-LINEAR VIBRATION SYSTEMS EXEMPLIFIED BY DUFFING–VAN DER POL EQUATION

1998 ◽  
Vol 213 (5) ◽  
pp. 907-914 ◽  
Author(s):  
A.Y.T. Leung ◽  
Q.C. Zhang
Keyword(s):  
Normal Form ◽  
Linear Vibration ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Non Linear

scholarly journals Simplification of weakly nonlinear systems and analysis of cardiac activity using them

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Irada Dzhalladova ◽  
Miroslava Růžičková
Keyword(s):  
Nonlinear System ◽  
Normal Form ◽  
Cardiac Activity ◽  
Original Method ◽  
System Of Differential Equations ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Established Method ◽  
Weakly Nonlinear ◽  
Bogolyubov Method

<p style='text-indent:20px;'>The paper deals with the transformation of a weakly nonlinear system of differential equations in a special form into a simplified form and its relation to the normal form and averaging. An original method of simplification is proposed, that is, a way to determine the coefficients of a given nonlinear system in order to simplify it. We call this established method the degree equalization method, it does not require integration and is simpler and more efficient than the classical Krylov-Bogolyubov method of normalization. The method is illustrated with several examples and provides an application to the analysis of cardiac activity modelled using van der Pol equation.</p>

Non-Linear Vibration Technique for Crack Detection in Beam Structures Using Frequency Mixing

2010 ◽  
Vol 96 (5) ◽  
pp. 977-980 ◽  
Author(s):  
E. Douka ◽  
K. A. Zacharias ◽  
L. J. Hadjileontiadis ◽  
A. Trochidis
Keyword(s):  
Crack Detection ◽  
Linear Vibration ◽  
Beam Structures ◽  
Vibration Technique ◽  
Non Linear ◽  
Frequency Mixing

NON-LINEAR VIBRATION ABSORBERS USING HIGHER ORDER INTERNAL RESONANCES

2000 ◽  
Vol 234 (5) ◽  
pp. 799-817 ◽  
Author(s):  
P.FRANK PAI ◽  
BERND ROMMEL ◽  
MARK J. SCHULZ
Keyword(s):  
Higher Order ◽  
Vibration Absorbers ◽  
Linear Vibration ◽  
Internal Resonances ◽  
Non Linear

scholarly journals On Periodic Perturbations of Asymmetric Duffing–Van-der-Pol Equation

2014 ◽  
Vol 24 (05) ◽  
pp. 1450061 ◽  
Author(s):  
Albert D. Morozov ◽  
Olga S. Kostromina
Keyword(s):  
Saddle Point ◽  
Limit Cycles ◽  
Small Neighborhood ◽  
Integrable Equation ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Periodic Perturbations ◽  
Autonomous Equation ◽  
Nonautonomous Equation ◽  
Time Periodic

Time-periodic perturbations of an asymmetric Duffing–Van-der-Pol equation close to an integrable equation with a homoclinic "figure-eight" of a saddle are considered. The behavior of solutions outside the neighborhood of "figure-eight" is studied analytically. The problem of limit cycles for an autonomous equation is solved and resonance zones for a nonautonomous equation are analyzed. The behavior of the separatrices of a fixed saddle point of the Poincaré map in the small neighborhood of the unperturbed "figure-eight" is ascertained. The results obtained are illustrated by numerical computations.

scholarly journals Inducing bistability with local electret technology in a microcantilever based non-linear vibration energy harvester

2013 ◽  
Vol 102 (15) ◽  
pp. 153901 ◽  
Author(s):  
M. López-Suárez ◽  
J. Agustí ◽  
F. Torres ◽  
R. Rurali ◽  
G. Abadal
Keyword(s):  
Energy Harvester ◽  
Vibration Energy ◽  
Linear Vibration ◽  
Vibration Energy Harvester ◽  
Non Linear

On Integrating Factors and a Perturbation Method

1995 ◽  
Author(s):  
W. T. van Horssen
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
First Integrals ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Integrating Factors ◽  
Complete Solutions

Abstract In this paper the fundamental concept (due to Euler, 1734) of how to make a first order ordinary differential equation exact by means of integrating factors, is extended to n-th order (n ≥ 2) ordinary differential equations and to systems of first order ordinary differential equations. For new classes of differential equations first integrals or complete solutions can be constructed. Also a perturbation method based on integrating factors can be developed. To show how this perturbation method works the method is applied to the well-known Van der Pol equation.

Vortex-Induced Vibrations of a Rigid Cylinder on Non-Linear Elastic Supports

2006 ◽  
Author(s):  
S. Bourdier ◽  
J. R. Chaplin
Keyword(s):  
Circular Cylinder ◽  
Phase Flow ◽  
Linear Vibration ◽  
Chaotic Motions ◽  
Frequency Spectra ◽  
Elastic Supports ◽  
Linear Elastic ◽  
Vortex Induced Vibrations ◽  
Non Linear ◽  
Insight Into

The dynamics of vortex-induced vibrations of a rigid circular cylinder with structural non-linearities, introduced by means of discontinuities in the support system, are studied experimentally. The analysis of the measurements is carried out using non-linear vibration tools, i.e phase-flow portraits, frequency spectra, Lyapunov exponents and correlation dimensions, to provide an insight into the dynamical changes in the system brought about by restricting the motion. We show that chaotic motions can occur due to the structural non-linearities.

Sign in / Sign up

Export Citation Format

Share Document