Parametric Identification of Nonlinear Systems Using Chaotic Excitation

2007 ◽  
Vol 2 (3) ◽  
pp. 225-231 ◽  
Author(s):  
M. D. Narayanan ◽  
S. Narayanan ◽  
Chandramouli Padmanabhan
Keyword(s):  
Time Series ◽  
Nonlinear Systems ◽  
Periodic Orbits ◽  
Parametric Identification ◽  
System Response ◽  
Unstable Periodic Orbits ◽  
Single Degree Of Freedom ◽  
System Parameters ◽  
Single Degree ◽  
Quadratic Damping

The use of a time series, which is the chaotic response of a nonlinear system, as an excitation for the parametric identification of single-degree-of-freedom nonlinear systems is explored in this paper. It is assumed that the system response consists of several unstable periodic orbits, similar to the input, and hence a Fourier series based technique is used to extract these nearly periodic orbits. Criteria to extract these orbits are developed and a least-squares problem for the identification of system parameters is formulated and solved. The effectiveness of this method is illustrated on a system with quadratic damping and a system with Duffing nonlinearity.

Nonlinear Parametric Identification Using Chaotic Data

1995 ◽  
Vol 1 (3) ◽  
pp. 291-305 ◽  
Author(s):  
N. Van de Wouw ◽  
G. Verbeek ◽  
D.H. Van Campen
Keyword(s):  
Time Series ◽  
Numerical Computation ◽  
Periodic Orbits ◽  
Nonlinear Dynamical System ◽  
Parametric Identification ◽  
Chaotic Time Series ◽  
Unstable Periodic Orbits ◽  
Estimation Process ◽  
Identification Method ◽  
Nonlinear Parametric Identification

The subject of this paper is the development of a nonlinear parametric identification method using chaotic data. In former research, the main problem in using chaotic data in parameter estimation appeared to be the numerical computation of the chaotic trajectories. This computational problem is due to the highly unstable character of the chaotic orbits. The method proposed in this paper is based on assumed physical models and has two important components. First, the chaotic time series is characterized by a "skeleton" of unstable periodic orbits. Second, these unstable periodic orbits are used as the input information for a nonlinear parametric identification method using periodic data. As a consequence, problems concerning the numerical computation of chaotic trajectories are avoided. The identifiability of the system is optimized by using the structure of the phase space instead of a single physical trajectory in the estimation process. Furthermore, before starting the estimation process, a huge data reduction has been accomplished by extracting the unstable periodic orbits from the long chaotic time series. The method is validated by application to a parametrically excited pendulum, which is an experimental nonlinear dynamical system in which transient chaos occurs.

The Response of Nonlinear Systems to Modulated High-Frequency Input

1993 ◽  
Author(s):  
S. A. Nayfeh ◽  
A. H. Nayfeh
Keyword(s):  
Nonlinear Systems ◽  
Natural Frequency ◽  
Amplitude Modulation ◽  
Carrier Frequency ◽  
High Frequency ◽  
Degree Of Freedom ◽  
Resonant Excitation ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Different Types

Abstract We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.

A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Bin Tang ◽  
M. J. Brennan
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Dependent Term ◽  
Quadratic Damping

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration.

The Measurement of Nonlinear Damping in Single-Degree-of-Freedom Systems

1991 ◽  
Vol 113 (1) ◽  
pp. 132-140 ◽  
Author(s):  
H. J. Rice ◽  
J. A. Fitzpatrick
Keyword(s):  
Nonlinear Distortion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Crucial Importance ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Wide Range ◽  
Impulse Excitation ◽  
Excitation Techniques ◽  
Quadratic Damping

The measurement and correct modelling of damping is of crucial importance in the prediction of the dynamical performance of systems for a wide range of engineering applications. In most cases, however, the experimental methods used to measure damping coefficients are extremely basic and, in general, poorly reported. This paper shows that damping is a deceptive parameter which is prone to subtle nonlinear distortion which often appears to satisfy general linear criteria. An efficient experimental method which provides for the measurement of both the linear and nonlinear damping for a single-degree-of-freedom system is proposed. The results from a numerical simulation study of a model with “drag” type quadratic damping are shown to give reliable estimates of parameters of the system when both random and impulse excitation techniques are used.

An Analysis of Pulse Control for Simple Mechanical Systems

1985 ◽  
Vol 107 (2) ◽  
pp. 123-131 ◽  
Author(s):  
Z. Prucz ◽  
T. T. Soong ◽  
A. Reinhorn
Keyword(s):  
Control Algorithm ◽  
Control Method ◽  
Excitation Frequency ◽  
Mechanical Systems ◽  
System Response ◽  
Control Parameters ◽  
Pulse Control ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
On Line

An efficient pulse control method for insuring safety of simple mechanical systems is developed and its sensitivity to the excitation frequency content and to various control parameters is studied. The control algorithm, consisting of applying pulse forces in a feedback fashion, is designed to insure that maximum system response is limited to safe values at all times. It is shown that the proposed algorithm is simple to implement and is efficient in controlling peak response in terms of on-line computation and pulse energy required. The technique is illustrated and analyzed for a single-degree-of-freedom linear system.

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