Oscillations And Resonances
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Oscillations And Resonances
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Author : Sergey G. Glebov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-04-10
Oscillations And Resonances written by Sergey G. Glebov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-10 with Mathematics categories.
This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators
Physical Fundamentals Of Oscillations
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Author : Leonid Chechurin
language : en
Publisher: Springer
Release Date : 2018-04-16
Physical Fundamentals Of Oscillations written by Leonid Chechurin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-16 with Technology & Engineering categories.
The book introduces possibly the most compact, simple and physically understandable tool that can describe, explain, predict and design the widest set of phenomena in time-variant and nonlinear oscillations. The phenomena described include parametric resonances, combined resonances, instability of forced oscillations, synchronization, distributed parameter oscillation and flatter, parametric oscillation control, robustness of oscillations and many others. Although the realm of nonlinear oscillations is enormous, the book relies on the concept of minimum knowledge for maximum understanding. This unique tool is the method of stationarization, or one frequency approximation of parametric resonance problem analysis in linear time-variant dynamic systems. The book shows how this can explain periodic motion stability in stationary nonlinear dynamic systems, and reveals the link between the harmonic stationarization coefficients and describing functions. As such, the book speaks the language of control: transfer functions, frequency response, Nyquist plot, stability margins, etc. An understanding of the physics of stability loss is the basis for the design of new oscillation control methods for, several of which are presented in the book. These and all the other findings are illustrated by numerical examples, which can be easily reproduced by readers equipped with a basic simulation package like MATLAB with Simulink. The book offers a simple tool for all those travelling through the world of oscillations, helping them discover its hidden beauty. Researchers can use the method to uncover unknown aspects, and as a reference to compare it with other, for example, abstract mathematical means. Further, it provides engineers with a minimalistic but powerful instrument based on physically measurable variables to analyze and design oscillatory systems.
Resonance Oscillations In Mechanical Systems
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Author : R. M. Evan-Iwanowski
language : en
Publisher: Elsevier Science & Technology
Release Date : 1976
Resonance Oscillations In Mechanical Systems written by R. M. Evan-Iwanowski and has been published by Elsevier Science & Technology this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mechanical vibration categories.
The Mechanics Of Nonlinear Systems With Internal Resonances
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Author : Arkadiy I. Manevich
language : en
Publisher: World Scientific
Release Date : 2005
The Mechanics Of Nonlinear Systems With Internal Resonances written by Arkadiy I. Manevich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied.
Mechanical Resonance Free And Forced Shm Of A Torsional Pendulum
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Author : Laura Imperatori
language : en
Publisher: GRIN Verlag
Release Date : 2014-02-03
Mechanical Resonance Free And Forced Shm Of A Torsional Pendulum written by Laura Imperatori and has been published by GRIN Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-03 with Science categories.
Scientific Essay from the year 2012 in the subject Physics - Mechanics, , language: English, abstract: In order to test SHM, the behaviour changes of a torsion pendulum due to different damping factors as well as its changes due to applying an external exciter were observed and compared with the theoretical expectations. The quality factor of the same damping state (with a brake current of 6A in the eddy brakes) was calculated using two different approaches and the resulting values were found to be within ơ of each one, as Q1 = 6.0±1.3 and Q2 = 7.5±0.7. The first approach was based on measuring the maximum displacement for each successive oscillation and deducing the slope from the plot of the natural logarithm of the amplitude against the number of oscillations. Differently, the second estimate of Q was obtained under forced oscillation conditions by taking the ratio of the experimentally determined resonance amplitude and the amplitude of natural oscillation.
Waves And Oscillations 2ed
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Author : N Subrahmanyam
language : en
Publisher: Vikas Publishing House
Release Date : 2009-11-01
Waves And Oscillations 2ed written by N Subrahmanyam and has been published by Vikas Publishing House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-01 with Science categories.
The subject matter is divided into twelve chapters. Each chapter is self-contained and is treated in a comprehensive way, using the S.I. system of units. Harmonic Oscillators, Linearity and Superposition Principle, Oscillations with One Degree of Freedom, Resonance and Sharpness of Resonance, Quality Factor, Doppler Effect in Sound and Light, Medical Applications of Ultrasonics, Acoustic Intensity, Acoustic Measurements, Wave Velocity and Group Velocity, Maxwells Equations, Propagation of Electromagnetic Waves in Isotropic Media, De Broglie Waves, Heisenbergs Uncertainty Principle and Special Theory of Relatively are some of the important topics which have been given special attention. Solved numerical problems, wherever necessary, are given in the text and in the exercises at the end of each chapter. The book is intended to be a textbook for the undergraduate students of Indian universities.
Mathematical Theory Of Scattering Resonances
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Author : Semyon Dyatlov
language : en
Publisher:
Release Date : 2019
Mathematical Theory Of Scattering Resonances written by Semyon Dyatlov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Frequencies of oscillating systems categories.
Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros.
Oscillations
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Author : Ian Benjamin Hopley
language : en
Publisher:
Release Date : 1972
Oscillations written by Ian Benjamin Hopley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Science categories.
Magnetization Oscillations And Waves
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Author : A.G. Gurevich
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Magnetization Oscillations And Waves written by A.G. Gurevich and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Science categories.
Written by two well-known researchers in the field, this useful reference takes an applied approach to high frequency processes including oscillations and waves in ferromagnets, antiferromagnets, and ferrimagnets. Problems evaluated include ferromagnetic and antiferromagnetic resonances, spin waves, nonlinear processes, and high frequency manifestations of interactions between the magnetic system and other systems of magnetically ordered substances as elastic waves and charge carriers. Unlike previous monographs on this subject, which are highly theoretical and written for very advanced readers, this book requires only an average college background in mathematics and experimental physics. It will be a valuable addition to the library of engineers and scientists in research and development for communications applications, and scientists interested in nonlinear magnetic phenomena. It also serves as an excellent introduction to the topic for newcomers in the field. Magnetization Oscillations and Waves not only presents results but also shows readers how to obtain them; most formulas are derived with so many details that readers can reproduce them. The book includes many summaries and tables and detailed references to significant work in the area by European researchers.
Nonlinear Resonances
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Author : Shanmuganathan Rajasekar
language : en
Publisher: Springer
Release Date : 2015-11-30
Nonlinear Resonances written by Shanmuganathan Rajasekar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-30 with Science categories.
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques involved in numerical simulations. Though primarily intended for graduate students, it can also be considered a reference book for any researcher interested in the dynamics of resonant phenomena.