Oscillations And Resonances

Author : Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 357 pages
File Size : 54,7 Mb
Release : 2017-04-10
Category : Mathematics
ISBN : 9783110335682

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Oscillations and Resonances by Sergey G. Glebov,Oleg M. Kiselev,Nikolai N. Tarkhanov Pdf

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

Author : Jiri Lebl
Publisher : Unknown
Page : 468 pages
File Size : 46,9 Mb
Release : 2019-11-13
Category : Electronic
ISBN : 1706230230

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Notes on Diffy Qs by Jiri Lebl Pdf

Version 6.0. An introductory course on differential equations aimed at engineers. The book covers first order ODEs, higher order linear ODEs, systems of ODEs, Fourier series and PDEs, eigenvalue problems, the Laplace transform, and power series methods. It has a detailed appendix on linear algebra. The book was developed and used to teach Math 286/285 at the University of Illinois at Urbana-Champaign, and in the decade since, it has been used in many classrooms, ranging from small community colleges to large public research universities. See https: //www.jirka.org/diffyqs/ for more information, updates, errata, and a list of classroom adoptions.

Author : R. M. Evan-Iwanowski
Publisher : Elsevier Science & Technology
Page : 316 pages
File Size : 40,7 Mb
Release : 1976
Category : Mechanical vibration
ISBN : STANFORD:36105030271774

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Resonance Oscillations in Mechanical Systems by R. M. Evan-Iwanowski Pdf

Author : Arnt Inge Vistnes
Publisher : Springer
Page : 576 pages
File Size : 52,8 Mb
Release : 2018-08-21
Category : Science
ISBN : 9783319723143

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Physics of Oscillations and Waves by Arnt Inge Vistnes Pdf

In this textbook a combination of standard mathematics and modern numerical methods is used to describe a wide range of natural wave phenomena, such as sound, light and water waves, particularly in specific popular contexts, e.g. colors or the acoustics of musical instruments. It introduces the reader to the basic physical principles that allow the description of the oscillatory motion of matter and classical fields, as well as resulting concepts including interference, diffraction, and coherence. Numerical methods offer new scientific insights and make it possible to handle interesting cases that can’t readily be addressed using analytical mathematics; this holds true not only for problem solving but also for the description of phenomena. Essential physical parameters are brought more into focus, rather than concentrating on the details of which mathematical trick should be used to obtain a certain solution. Readers will learn how time-resolved frequency analysis offers a deeper understanding of the interplay between frequency and time, which is relevant to many phenomena involving oscillations and waves. Attention is also drawn to common misconceptions resulting from uncritical use of the Fourier transform. The book offers an ideal guide for upper-level undergraduate physics students and will also benefit physics instructors. Program codes in Matlab and Python, together with interesting files for use in the problems, are provided as free supplementary material.

Author : Helmut Wiedemann
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 47,7 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783662029039

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Particle Accelerator Physics by Helmut Wiedemann Pdf

Particle Accelerator Physics covers the dynamics of relativistic particle beams, basics of particle guidance and focusing, lattice design, characteristics of beam transport systems and circular accelerators. Particle-beam optics is treated in the linear approximation including sextupoles to correct for chromatic aberrations. Perturbations to linear beam dynamics are analyzed in detail and correction measures are discussed, while basic lattice design features and building blocks leading to the design of more complicated beam transport systems and circular accelerators are studied. Characteristics of synchrotron radiation and quantum effects due to the statistical emission of photons on particle trajectories are derived and applied to determine particle-beam parameters. The discussions specifically concentrate on relativistic particle beams and the physics of beam optics in beam transport systems and circular accelerators such as synchrotrons and storage rings. This book forms a broad basis for further, more detailed studies of nonlinear beam dynamics and associated accelerator physics problems, discussed in the subsequent volume.

Author : Aman Kalsi,Nikhail Balani
Publisher : Cambridge University Press
Page : 129 pages
File Size : 54,5 Mb
Release : 2016-03-31
Category : Medical
ISBN : 9781107498334

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Physics for the Anaesthetic Viva by Aman Kalsi,Nikhail Balani Pdf

A concise book that conveys the essential physics concepts required to pass the FRCA viva examinations, with relevant applied questions.

Author : Arkadiy I. Manevich,Leonid Isaakovich Manevich
Publisher : World Scientific
Page : 278 pages
File Size : 55,7 Mb
Release : 2005
Category : Science
ISBN : 9781860945106

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The Mechanics of Nonlinear Systems with Internal Resonances by Arkadiy I. Manevich,Leonid Isaakovich Manevich Pdf

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.

Author : Laura Imperatori
Publisher : GRIN Verlag
Page : 9 pages
File Size : 45,7 Mb
Release : 2014-02-03
Category : Science
ISBN : 9783656586029

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Mechanical Resonance. Free and forced SHM of a torsional pendulum by Laura Imperatori Pdf

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.

Author : A.G. Gurevich,G.A. Melkov
Publisher : CRC Press
Page : 460 pages
File Size : 51,6 Mb
Release : 2020-12-17
Category : Science
ISBN : 9780429605758

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Magnetization Oscillations and Waves by A.G. Gurevich,G.A. Melkov Pdf

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.

Author : David Alʹbertovich Frank-Kamenet︠s︡kiĭ
Publisher : Unknown
Page : 28 pages
File Size : 43,7 Mb
Release : 1961
Category : Plasma oscillations
ISBN : MINN:31951D03596225W

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Eigen Oscillations of a Bound Plasma by David Alʹbertovich Frank-Kamenet︠s︡kiĭ Pdf

Author : Leonid Chechurin,Sergej Chechurin
Publisher : Springer
Page : 264 pages
File Size : 45,9 Mb
Release : 2018-04-16
Category : Technology & Engineering
ISBN : 9783319751542

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Physical Fundamentals of Oscillations by Leonid Chechurin,Sergej Chechurin Pdf

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.

Author : N Subrahmanyam
Publisher : Vikas Publishing House
Page : 448 pages
File Size : 52,9 Mb
Release : 2009-11-01
Category : Science
ISBN : 9780706985436

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Waves And Oscillations 2Ed by N Subrahmanyam Pdf

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, Maxwell’s Equations, Propagation of Electromagnetic Waves in Isotropic Media, De Broglie Waves, Heisenberg’s 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.

Author : Ian Benjamin Hopley
Publisher : Unknown
Page : 76 pages
File Size : 52,6 Mb
Release : 1972
Category : Science
ISBN : STANFORD:36105030220961

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Oscillations by Ian Benjamin Hopley Pdf

Author : Arkadiy I. Manevich,Leonid Isaakovich Manevich
Publisher : World Scientific
Page : 276 pages
File Size : 42,7 Mb
Release : 2005
Category : Science
ISBN : 9781860945106

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The Mechanics of Nonlinear Systems with Internal Resonances by Arkadiy I. Manevich,Leonid Isaakovich Manevich Pdf

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.

Author : Ali H. Nayfeh,Dean T. Mook
Publisher : John Wiley & Sons
Page : 720 pages
File Size : 53,6 Mb
Release : 2008-09-26
Category : Science
ISBN : 9783527617593

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Nonlinear Oscillations by Ali H. Nayfeh,Dean T. Mook Pdf

Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses simple physical examples to explain nonlinear dispersive and nondispersive waves. The notation is unified and the analysis modified to conform to discussions. Solutions are worked out in detail for numerous examples, results are plotted and explanations are couched in physical terms. The book contains an extensive bibliography.