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2 edition of Perturbation analysis of nonlinear oscillations using symbolic and numberical computations found in the catalog.

Perturbation analysis of nonlinear oscillations using symbolic and numberical computations

Mohammad Bagher Dadfar

Perturbation analysis of nonlinear oscillations using symbolic and numberical computations

by Mohammad Bagher Dadfar

  • 136 Want to read
  • 22 Currently reading

Published .
Written in English

    Subjects:
  • Perturbation (Mathematics),
  • Nonlinear oscillations.

  • Edition Notes

    Statementby Mohammad Bagher Dadfar.
    Series[Ph. D. theses / State University of New York at Binghamton -- no. 572], Ph. D. theses (State University of New York at Binghamton) -- no. 572.
    The Physical Object
    Paginationix, 134 leaves :
    Number of Pages134
    ID Numbers
    Open LibraryOL21918890M

    The Hamiltonian structure of the nonlinear Schr¨odinger equation (b), the beam and membrane equation (c), the KdV and the Euler equation (d) are presented in the Appendix. In these Notes we shall adopt the point of view of regarding the Nonlinear Wave equation (2) as an Infinite Dimensional Hamiltonian System, focusing. A systematic perturbation theory is presented for the analysis of nonlinear problems. The lowest‐order result is just that obtained by linearizing the problem, and the higher‐order terms are the solutions of inhomogeneous linear problems. The essential feature of the method is the procedure for avoiding secular terms, which is based on the Lindstedt‐Poincaré technique Cited by:

    Symbolic computation in nonlinear control system modeling and analysis Citation for published version (APA): Jager, de, A. G. (). Symbolic computation in nonlinear control system modeling and analysis. In Proceedings of the IEEE International Symposium on Computer Aided Control System Design, August , , Hawai, USA (pp. ).Cited by: 2. A Brief Introduction to Nonlinear Vibrations Anindya Chatterjee Mechanical Engineering, Indian Institute of Science, Bangalore some numerical results for the above nonlinear oscillations of Eq. 1, as compared with the obtainable via a singula r perturbation scheme. One.

    Notes on Perturbation Techniques for ODEs James A. Tzitzouris The idea behind the perturbation method is a simple one. Faced with a problem that we cannot solve exactly, but that is close (in some sense) to an auxiliary problem that we can solve exactly, aFile Size: KB. perturbation approximations, because perturbation analysis does not give the user the tools to relocate these problems to areas of the state space that are of no importance.1 Consequently, the undesirable oscillations could occur close to the steady state. To understand the problem, consider the following policy function: x= f(x 1) = 0 +x 1.


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Perturbation analysis of nonlinear oscillations using symbolic and numberical computations by Mohammad Bagher Dadfar Download PDF EPUB FB2

A self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since Begins with fundamental concepts and techniques of analysis and progresses through recent developments.

Provides an overview that abstracts and introduces main nonlinear phenomena.5/5(1). 5 Forced Oscillations Introduction Forced Oscillations of Linear Systems Combination Tones Subharmonic Oscillations Iteration Methods for Harmonic Oscillations without Damping Perturbation Theory Applied to Forced Oscillations Worked Examples Using the Perturbation Method Introduction to singular perturbation methods Nonlinear oscillations This text is part of a set of lecture notes written by A.

Aceves, N. Ercolani, C. Jones, J. Lega & J. Moloney, for a summer school held in Cork, Ireland, from to The links below will take you to online overviews of some of the concepts used Size: KB. Nonlinear Oscillation Up until now, we’ve been considering the di erential equation for the (damped) harmonic oscillator, y + 2 y_ +!2y= L y= f(t): (1) Due to the linearity of the di erential operator on the left side of our equation, we were able to make use of a large number of theorems in nding the solution to this Size: KB.

An Introduction to Nonlinear Oscillations. Ronald E. Mickens limit cycle linear second-order linearly independent Mathematical McGraw-Hill multi-time nonlinear differential equation nonlinear equation Nonlinear Oscillations obtain periodic solutions Ordinary Differential Equations particular solution pendulum period 27r All Book Search.

Singh et al. e Figure 2: Panel (a): a 1 coefficients obtained by DFS calculation for the periodic oscillations of the pendulum shows an almost linear variation with θ small angles the motion of the simple pendulum is described by θ m cos(ωt).As the angle of displacement increases, a 1 is found to decrease (trend is given by Eq.

(9)). The (b) variation of aAuthor: Inderpreet Singh, Palakkandy Arun, Fabio Lima. As a supplement, an asymptotic analysis of nonlinear dynamics of long-wave perturbations superimposed on a damped by small viscosity Kolmogorov flow (very large, but finite Reynolds numbers) is made.

Nonlinear Oscillations by Nicholas Minorsky (Author) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book.

The 13 Format: Hardcover. The modes are extracted from sensor data or data provided by simulation outputs of power system oscillations by using the Koopman mode analysis that is based on a fully nonlinear spectral theory.

A self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since Begins with fundamental concepts and techniques of analysis and progresses through recent developments.

Provides an overview that abstracts and introduces main nonlinear phenomena. Treats systems having a single degree of freedom. clearer in the course of the analysis, such a desirable transformation can be generated by using the generating vector W(x; q), defined by the differential equations whose initial conditions at q = 0 are x = x(t; E).

Note that 7 is a varying small parameter and we seek solutions at q = E. - 7File Size: KB. An intrinsic method of harmonic analysis for application to problems concerning non-linear periodic oscillations is presented. The method is designed to overcome the observed shortcomings of the conventional method of harmonic balance, and it is described with the aid of an example which was used earlier to demonstrate the inconsistency of the results obtained Cited by:   Asymptotic recurrence formulas for treating nonlinear oscillation problems are presented.

These formulas are based on a Lie transform similar to that described by Deprit for Hamiltonian systems. It is shown that the basic formulas have essentially the same forms as those obtained by Deprit and by the present author in the Hamiltonian by: Nonlinear Oscillations is a quarterly peer-reviewed mathematical journal that was established in It is published by Springer Science+Business Media on behalf of the Institute of Mathematics, National Academy of Sciences of covers research in the qualitative theory of differential or functional differential includes the qualitative analysis of Discipline: Mathematics.

By coupling the Lindstedt-Poincaré perturbation technique with a rational approximation, we propose a method for summing up the perturbation solutions of the nonlinear oscillation of a conservative single-degree-of-freedom system.

The equation of motion contains a parameter. This method can represent the singularities of the period at certain values of the Cited by: The results listed in Table 1 show that the assumptions of Theorems 5 and 8 are satisfied. By Theorems 5 and 8, we can compute the relative perturbation bounds and, results averaged as the geometric mean of 10 randomly perturbed runs.

Some results are Cited by: 3. The nonlinear Duffing and Van der Pol oscillations will be taken as examples to illustrate the applicability and accuracy of the iteration procedure. 2 The iteration procedure Consider a nonlinear conservative oscillator described as x¨+f(x)=0,x(0)=A,x˙(0)=0, (1) where f(x)in a nonlinear function and has the property f(−x))=−f(x).

(2) Eq. In this paper we will study a nonlinear oscillator, which is governed by /I u + 1+u2 -0 (1) 6The paper was received on Communications in Nonlinear Science & Numerical Simulation Vo, No.2 (Jun. ) with initial conditions u(0) = A and u'(0) = by: nonlinear pendulum using a modified perturbation technique known as the homotopy perturbation method [16] proposed by J.

In this method, which requires neither a small parameter nor a linear term in the differential equation, an artificial perturbation equation is constructed by embedding an artificial parameter ε ∈ [0,1], which is. The objective of this paper is to present an analytical investigation to analyze the vibration of parametrically excited oscillator with strong cubic negative nonlinearity based on Mathieu-Duffing equation.

The analytic investigation was conducted by using He's homotopy-perturbation method (HPM). In order to obtain the analytical solution of Mathieu-Duffing equation, Cited by:.

our best knowledge, there has been no perturbation analysis for ()with>1 in the known literature. As a continuation of the previous results, the rest of the Section,somepreliminary lemmas are given. In Section, two perturbation bounds for the unique solution to () are derived. Furthermore, in Section.Nonlinear Inverse Perturbation Method in Dynamic Analysis Ki-Ook Kim,* William J.

Anderson,t and Robert E. SandstromJ The University of Michigan, Ann Arbor, Michigan An analytical method is presented for the automated redesign of the modal characteristics of .in the direction of analysis and control of nonlinear oscillations are presented with more details.

Some planned directions of research are brie y described in the third chapter. Diplomas and grades I have obtained three scienti c degrees in Russia, the last one is the full doctorAuthor: Denis Efimov.