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Harmonic Balance For Nonlinear Vibration Problems
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Book Synopsis Harmonic Balance for Nonlinear Vibration Problems by : Malte Krack
Download or read book Harmonic Balance for Nonlinear Vibration Problems written by Malte Krack and published by Springer. This book was released on 2019-03-23 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an introduction to Harmonic Balance for nonlinear vibration problems, covering the theoretical basis, its application to mechanical systems, and its computational implementation. Harmonic Balance is an approximation method for the computation of periodic solutions of nonlinear ordinary and differential-algebraic equations. It outperforms numerical forward integration in terms of computational efficiency often by several orders of magnitude. The method is widely used in the analysis of nonlinear systems, including structures, fluids and electric circuits. The book includes solved exercises which illustrate the advantages of Harmonic Balance over alternative methods as well as its limitations. The target audience primarily comprises graduate and post-graduate students, but the book may also be beneficial for research experts and practitioners in industry.
Book Synopsis Nonlinear Vibration with Control by : David Wagg
Download or read book Nonlinear Vibration with Control written by David Wagg and published by Springer Science & Business Media. This book was released on 2009-12-03 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors discuss the interrelationship of linear vibration theory for multi-degree-of-freedom systems; nonlinear dynamics and chaos; and nonlinear control. No other book covers these areas in the same way, so this is a new perspective on these topics.
Book Synopsis A Filtered High-dimensional Harmonic Balance Method for Problems in Nonlinear Dynamics by : Allen Russell LaBryer
Download or read book A Filtered High-dimensional Harmonic Balance Method for Problems in Nonlinear Dynamics written by Allen Russell LaBryer and published by . This book was released on 2009 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Incremental Harmonic Balance Method for Nonlinear Structural Vibrations by : Sai-ling Lau
Download or read book Incremental Harmonic Balance Method for Nonlinear Structural Vibrations written by Sai-ling Lau and published by . This book was released on 1982 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Incremental Harmonic Balance Method for Nonlinear Structural Vibrations by : Sai-Ling Lau
Download or read book Incremental Harmonic Balance Method for Nonlinear Structural Vibrations written by Sai-Ling Lau and published by . This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Analysis of Superharmonic Oscillations by : J. J. Wu
Download or read book On the Analysis of Superharmonic Oscillations written by J. J. Wu and published by . This book was released on 1992 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents an analysis for the superharmonics of a forced nonlinear vibration problem involving small parameters, using a generalized harmonic balance method. A nonlinear ordinary differential equation with several nonlinear terms and a periodic forcing function is considered. For the case of superharmonic oscillations of order 2, the key equations for the obtaining the information on the superharmonics will be derived, including a new, nonlinear ordinary differential equation of a slow varying function compared with the original dependent variable. Using these equations, the steady state solution and its stability behavior can be calculated. Results for a special set of parameters are obtained, including a stable node for the steady state solution and the associated van del Pol plane.
Book Synopsis The Behaviour of Nonlinear Vibrating Systems by : Wanda Szemplinska
Download or read book The Behaviour of Nonlinear Vibrating Systems written by Wanda Szemplinska and published by Springer Science & Business Media. This book was released on 1990-06-30 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide students, practicing engineers and scientists with a treatment of nonlinear phenomena occurring in physical systems. Although only mechanical models are used, the theory applies to all physical systems governed by the same equations, so that the book can be used to study nonlinear phenomena in other branches of engineering, such as electrical engineering and aerospace engineering, as well as in physics. The book consists of two volumes. Volume I is concerned with single degree-of-freedom systems and it presents the fundamental concepts of nonlinear analysis. Both analytical methods and computer simulations are included. The material is presented in such a manner that the book can be used as a graduate as well as an undergraduate textbook. Volume II deals with multi-degree-of-freedom systems. Following an introduc tion to linear systems, the volume presents fundamental concepts of geometric theory and stability of motion of general nonlinear systems, as well as a concise discussion of basic approximate methods for the response of such systems. The material represents a generalization of a series of papers on the vibration of nonlinear multi-degree-of-freedom systems, some of which were published by me and my associates during the period 1965 - 1983 and some are not yet published.
Book Synopsis The Behaviour of Nonlinear Vibrating Systems by : Wanda Szemplinska
Download or read book The Behaviour of Nonlinear Vibrating Systems written by Wanda Szemplinska and published by Springer. This book was released on 1990-06-30 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Duffing Equation by : Ivana Kovacic
Download or read book The Duffing Equation written by Ivana Kovacic and published by John Wiley & Sons. This book was released on 2011-02-11 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical techniques required to study nonlinear dynamics, helping the reader with little mathematical background to understand the text. The Duffing Equation provides a reference text for postgraduate and students and researchers of mechanical engineering and vibration / nonlinear dynamics as well as a useful tool for practising mechanical engineers. Includes a chapter devoted to historical background on Georg Duffing and the equation that was named after him. Includes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation. Contains a comprehensive treatment of the various forms of the Duffing equation. Uses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.
Book Synopsis Studies in Nonlinear Vibration Theory by : Courant Institute of Mathematical Sciences
Download or read book Studies in Nonlinear Vibration Theory written by Courant Institute of Mathematical Sciences and published by . This book was released on 1946 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Mechanical Vibrations by : P. Srinivasan
Download or read book Nonlinear Mechanical Vibrations written by P. Srinivasan and published by John Wiley & Sons. This book was released on 1995 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Study And Analysis Of Vibrations Have Found Lot Of Importance In Recent Years In Both Academic And Industrial Fields. Nonlinear Vibration In Particular, Has Developed Into A Discipline. The Approach In This Book Is To Highlight And Treat The Essential Aspects Of Nonlinear Vibrations At A Level Useful To Both Students And Practicing Engineers.Design, Development And Utilisation Of Most Active Systems/Equipments (I.E., Those With Movable Parts) Must Address Vibration Impact On Their Performance. Understanding Of Vibration Will Help Minimise The Impact Of Undesirable Vibrations And Use Vibrations To Advantage, Where Possible, Considering Applications Both Commonplace And In Highly Sophisticated Hi-Tech Areas Like Aerospace, Automated/Robot Controlled Production Industries, Etc.This Book Is Written To Convey Succinctly And Clearly The Various Aspects Of Nonlinear Vibrations Through A Judicious Choice Of Text Material, Profusely Illustrating Important Points, And Giving A Mathematical Tinge At A Level Easily Grasped By A Graduate/Undergraduate Student. As All Engineering Ideas Normally Culminate Into A Hardware Hem, This Book Will Serve All Interdisciplinary Fields Of Engineering.
Book Synopsis The Method of Normal Forms by : Ali H. Nayfeh
Download or read book The Method of Normal Forms written by Ali H. Nayfeh and published by John Wiley & Sons. This book was released on 2011-08-29 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this introductory treatment Ali Nayfeh presents different concepts from dynamical systems theory and nonlinear dynamics in a rigorous yet plan way. He systematically introduces models and techniques and states the relevant ranges of validity and applicability. The reader is provided with a clear operational framework for consciously use rather than focused on the underlying mathematical apparatus. The exposition is largely by means of examples, dealt with up to their final outcome. For most of the examples, the results obtained with the method of normal forms are equivalent to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging. The previous edition had a remarkable success by researchers from all over the world working in the area of nonlinear dynamics and their applications in engineering. Additions to this new edition concern major topics of current interest. In particular, the author added three new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems. In particular the latter has become of major importance in several applications, both in mechanics and in different areas. Accessible to engineers and applied scientist involved with nonlinear dynamics and their applications in a wide variety of fields. It is assumed that readers have a knowledge of basic calculus as well as the elementary properties of ordinary-differential equations.
Book Synopsis Calm, Smooth and Smart by : Peter Eberhard
Download or read book Calm, Smooth and Smart written by Peter Eberhard and published by Springer Nature. This book was released on 2023-09-19 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains and summarizes research carried out within the DFG Priority Programme 1897: "Calm, Smooth and Smart - Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation". The contributions help reduce unwanted vibrations by developing novel approaches for influencing them and lead to a “calm, smooth and smart” behaviour of technical units. “Calm” represents the demand to avoid or at least to severely reduce unwanted noise generated by technical installations. “Smooth” ensures a still comfortable and jerk-free operation of them. Finally, “smart” means that the introduced damping devices not only help to achieve the desired vibrational behaviour of the overall technical systems, but also that they take over additional functional tasks. The results presented in this volume summarize the state-of-the-art and provide motivation for future research. The book is intended for experienced researchers as well as for doctoral and post-doctoral students in engineering, mathematics and physics, as well as industrial researchers interested in the field.
Book Synopsis Nonlinearity in Structural Dynamics by : K Worden
Download or read book Nonlinearity in Structural Dynamics written by K Worden and published by CRC Press. This book was released on 2019-04-23 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many types of engineering structures exhibit nonlinear behavior under real operating conditions. Sometimes the unpredicted nonlinear behavior of a system results in catastrophic failure. In civil engineering, grandstands at sporting events and concerts may be prone to nonlinear oscillations due to looseness of joints, friction, and crowd movements.
Book Synopsis Nonlinear Structures & Systems, Volume 1 by : Matthew R.W. Brake
Download or read book Nonlinear Structures & Systems, Volume 1 written by Matthew R.W. Brake and published by Springer Nature. This book was released on 2022-07-28 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Structures & Systems, Volume 1: Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022, the first volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Experimental Nonlinear Dynamics Jointed Structures: Identification, Mechanics, Dynamics Nonlinear Damping Nonlinear Modeling and Simulation Nonlinear Reduced-Order Modeling Nonlinearity and System Identification
Book Synopsis Computation of Nonlinear Modes of Vibration of Systems Undergoing Unilateral Contact Through the Semi-smooth Newton Approach by : Yulin Shi
Download or read book Computation of Nonlinear Modes of Vibration of Systems Undergoing Unilateral Contact Through the Semi-smooth Newton Approach written by Yulin Shi and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "In structural dynamics, autonomous conservative systems most commonly exhibit continuous families of periodic orbits in the phase space, usually known as modes of vibration. The main task of modal analysis is to accurately compute natural frequencies and corresponding mode shapes of vibratory mechanical systems as they are known, at least in a linear context, to properly predict the conditions under which the associated periodically forced systems will resonate. Characterizing the modes of vibration of nonlinear yet smooth mechanical systems (systems governed by ordinary differential equations that are smooth with respect to the unknown displacement and velocity), such as Duffing oscillators, is a current topic of interest in the industrial and academic spheres. Many useful tools, such as the finite element method, the harmonic balance method, the continuation techniques and the frequency-energy plots provide great assistance in understanding the modal dynamics. However, theoretical as well as numerical issues arise when extending these tools to nonsmooth problems, such as unilateral contact and frictional formulations. The mathematical nature of these terms is such that the use of conventional nonlinear solvers such as Newton's method is questionable. In this work, unilateral contact conditions are considered. Their common complementarity form is expressed as the root set of semismooth functions. In statics, the solution can thus be retrieved through the semismooth version of Newton's method for which convergence rates can be derived. In vibration analysis, in the frameworks of either periodically forced or autonomous dynamics, a periodic solution is assumed and the proposed semismooth form of the unilateral contact conditions allows for the straightforward implementation of Galerkin-like methods such as the harmonic balance method. The resulting nonlinear equations stemming from Galerkin projection on the Fourier basis are still semismooth thus solvable using semismooth Newton's method. Arclength continuation is then implemented to follow the solution branches displayed in Frequency-Energy plots. For comparison purposes, time-marching solutions serve as references. It is demonstrated that the proposed formulation is capable of capturing the main vibratory resonances, the sub-harmonic resonances as well as the internal resonances known to emanate in nonlinear dynamics. The proposed algorithms can be extended to finding the modes of vibration of mechanical bodies with arbitrary shapes and challenging contact interfaces using the finite element method. In Appendix B, a theoretical question on the meaning of the forced responses found via the harmonic balance method is raised but remains unanswered." --
Book Synopsis Strongly Nonlinear Oscillators by : Livija Cveticanin
Download or read book Strongly Nonlinear Oscillators written by Livija Cveticanin and published by Springer. This book was released on 2014-05-22 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for professionals and engineers who apply these techniques to the field of nonlinear oscillations.
