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

- 136 Want to read
- 22 Currently reading

Published
**1982**
.

Written in English

- Perturbation (Mathematics),
- Nonlinear oscillations.

**Edition Notes**

Statement | by 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 | |
---|---|

Pagination | ix, 134 leaves : |

Number of Pages | 134 |

ID Numbers | |

Open Library | OL21918890M |

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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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.

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(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.

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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.

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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.

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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.

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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.