Analysis on Critical Phenomena of a Hysteretic System

2003 ◽  
Author(s):  
Z. Chen ◽  
Z. Q. Wu ◽  
P. Yu
Keyword(s):  
Critical Phenomena ◽  
Nonlinear Dynamical Systems ◽  
Critical Phenomenon ◽  
External Forcing ◽  
Restoring Force ◽  
Nonlinear Dynamical ◽  
Hysteretic Property ◽  
Nonlinear Mechanical System ◽  
Hysteretic Damper ◽  
New Finding

In this paper, a nonlinear mechanical system with external forcing is investigated to study the critical phenomena of the system. The system involves a von der Pol type damping and a hysteretic damper representing a restoring force. Numerical simulations are used to show that under an external exciting force, the hysteretic restoring force may not follow the routes described by a conventional form of piecewise function, but exhibit some irregular behavior. We call this unusual situation the critical phenomenon of the system. Simulations results suggest that a device with hysteretic property (e.g., the damper considered in this paper) may change its typical characteristics under external forcing. This new finding may enhance the study of nonlinear dynamical systems with hysteretic property under external excitement.

A Frequency Domain Versus a Time Domain Identification Technique for Nonlinear Parameters Applied to Wire Rope Isolators

2000 ◽  
Vol 123 (4) ◽  
pp. 645-650 ◽  
Author(s):  
Gaetan Kerschen ◽  
Vincent Lenaerts ◽  
Stefano Marchesiello ◽  
Alessandro Fasana
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Nonlinear Dynamical Systems ◽  
Wire Rope ◽  
Restoring Force ◽  
Nonlinear Parameters ◽  
Nonlinear Dynamical ◽  
Domain Identification ◽  
Identification Technique ◽  
Reverse Path Method

The present paper aims to compare two techniques for identification of nonlinear dynamical systems. The Conditioned Reverse Path method, which is a frequency domain technique, is considered together with the Restoring Force Surface method, a time domain technique. Both methods are applied for experimental identification of wire rope isolators and the results are compared. Finally, drawbacks and advantages of each technique are underlined.

Refining the Method of Averaging for a More Accurate Analytical Approximation to the Behaviors of a Damped Pendulum

2012 ◽  
Author(s):  
Clark C. McGehee ◽  
Si Mohamed Sah ◽  
Brian P. Mann
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Damping ◽  
Analytical Approximation ◽  
Method Of Averaging ◽  
Restoring Force ◽  
Nonlinear Dynamical ◽  
Wide Range ◽  
Approximation Errors ◽  
Kbm Method

KBM averaging is a widely used technique in the analysis of nonlinear dynamical systems. The KBM method allows complex systems to be approximated as perturbations of simple harmonic oscillator. In many cases, such as in otherwise linear systems with various forms nonlinear damping, the KBM method performs exceptionally well, with error proportional to the size of the perturbations. However, when the largest perturbation in the system arises from nonlinearities in the restoring force, the KBM method falls short, and the interesting effects of other nonlinear terms are drowned out by the approximation errors generated by the KBM method. By generalizing the notion of KBM averaging and approximating systems as perturbations the isoenergy contours of their corresponding Hamiltonian, a greater degree of accuracy can be obtained. We extend the work of several authors to show that not only is this method more accurate, but it is also simple to implement and generalizable to a wide range of nonlinear systems. As an illustrative example, the motion of a pendulum on a tilted platform is studied.

Maximum entropy approach to the identification of stochastic reduced-order models of nonlinear dynamical systems

2010 ◽  
Vol 114 (1160) ◽  
pp. 637-650 ◽  
Author(s):  
M. Arnst ◽  
R. Ghanem ◽  
S. Masri
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Quantitative Description ◽  
Polynomial Expansion ◽  
Reduced Order Models ◽  
State Variables ◽  
Restoring Force ◽  
Nonlinear Dynamical ◽  
Entropy Maximization ◽  
Reduced Order

AbstractData-driven methodologies based on the restoring force method have been developed over the past few decades for building predictive reduced-order models (ROMs) of nonlinear dynamical systems. These methodologies involve fitting a polynomial expansion of the restoring force in the dominant state variables to observed states of the system. ROMs obtained in this way are usually prone to errors and uncertainties due to the approximate nature of the polynomial expansion and experimental limitations. We develop in this article a stochastic methodology that endows these errors and uncertainties with a probabilistic structure in order to obtain a quantitative description of the proximity between the ROM and the system that it purports to represent. Specifically, we propose an entropy maximization procedure for constructing a multi-variate probability distribution for the coefficients of power-series expansions of restoring forces. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed framework.

Design of a non-linear vibration absorber

2012 ◽  
Vol 3 (2) ◽  
pp. 111-115
Author(s):  
M. Geeroms ◽  
M. Marijns ◽  
M. Loccufier ◽  
D. Aeyels
Keyword(s):  
Nonlinear Vibration ◽  
Nonlinear Dynamical Systems ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Fourier Series Expansion ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Linear Vibration ◽  
Restoring Force ◽  
Nonlinear Dynamical

Linear vibration absorbers can only capture certain discrete frequencies. Therefore the useof nonlinear vibration absorbers which can capture a whole range of frequencies is investigated asan alternative. Such a nonlinear vibration absorber has some special characteristics. For examplethere is a certain frequency-energy dependence. To investigate nonlinear dynamical systems thereis a need for new methods. The harmonic balance method is such a method and is discussed. Theidea is to substitute a Fourier series expansion of the solution variables into the system equations and’balance’ them. Furthermore two realisations of a nonlinear energy sink as an example of a nonlinearvibration absorber are discussed. One based on the restoring force in a wire, the other one by forcinga linear spring to follow a certain path. As will be discussed, an analog principle can be used for therealisation of a Duffing type of nonlinear absorber.

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