Download or read book Lambda Matrices and Vibrating Systems written by Peter Lancaster and published by Elsevier. This book was released on 2014-07-10 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with latent vectors in common. The book then expounds on Lambda matrices and on some numerical methods for Lambda matrices. These methods explain developments of known approximations and rates of convergence. The text then addresses general solutions for simultaneous ordinary differential equations with constant coefficients. The results of some of the studies are then applied to the theory of vibration by applying the Lagrange method for formulating equations of motion, after the formula establishing the energies and dissipation functions are completed. The book describes the theory of resonance testing using the stationary phase method, where the test is carried out by applying certain forces to the structure being studied, and the amplitude of response in the structure is measured. The book also discusses other difficult problems. The text can be used by physicists, engineers, mathematicians, and designers of industrial equipment that incorporates motion in the design.
Download or read book Vibrations and Stability of Multiple Parameter Systems written by K. Huseyin and published by Springer Science & Business Media. This book was released on 1978-06-30 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Damped Oscillations of Linear Systems written by Krešimir Veselić and published by Springer Science & Business Media. This book was released on 2011-07-09 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and the perturbation of the time evolution.
Download or read book Vibration with Control written by Daniel J. Inman and published by John Wiley & Sons. This book was released on 2006-11-02 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers are becoming increasingly aware of the problems caused by vibration in engineering design, particularly in the areas of structural health monitoring and smart structures. Vibration is a constant problem as it can impair performance and lead to fatigue, damage and the failure of a structure. Control of vibration is a key factor in preventing such detrimental results. This book presents a homogenous treatment of vibration by including those factors from control that are relevant to modern vibration analysis, design and measurement. Vibration and control are established on a firm mathematical basis and the disciplines of vibration, control, linear algebra, matrix computations, and applied functional analysis are connected. Key Features: Assimilates the discipline of contemporary structural vibration with active control Introduces the use of Matlab into the solution of vibration and vibration control problems Provides a unique blend of practical and theoretical developments Contains examples and problems along with a solutions manual and power point presentations Vibration with Control is an essential text for practitioners, researchers, and graduate students as it can be used as a reference text for its complex chapters and topics, or in a tutorial setting for those improving their knowledge of vibration and learning about control for the first time. Whether or not you are familiar with vibration and control, this book is an excellent introduction to this emerging and increasingly important engineering discipline.
Download or read book Introduction to Matrix Computations written by G. W. Stewart and published by Elsevier. This book was released on 1973-06-15 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical linear algebra is far too broad a subject to treat in a single introductory volume. Stewart has chosen to treat algorithms for solving linear systems, linear least squares problems, and eigenvalue problems involving matrices whose elements can all be contained in the high-speed storage of a computer. By way of theory, the author has chosen to discuss the theory of norms and perturbation theory for linear systems and for the algebraic eigenvalue problem. These choices exclude, among other things, the solution of large sparse linear systems by direct and iterative methods, linear programming, and the useful Perron-Frobenious theory and its extensions. However, a person who has fully mastered the material in this book should be well prepared for independent study in other areas of numerical linear algebra.
Download or read book IUTAM Symposium on Asymptotics Singularities and Homogenisation in Problems of Mechanics written by A.B. Movchan and published by Springer. This book was released on 2006-05-09 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the IUTAM Symposium held in Liverpool, UK, 8-11 July 2002
Download or read book Analytic Perturbation Theory and Its Applications written by Konstantin E. Avrachenkov and published by SIAM. This book was released on 2013-12-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior?the so-called singularly perturbed problems. Analytic Perturbation Theory and Its Applications includes a comprehensive treatment of analytic perturbations of matrices, linear operators, and polynomial systems, particularly the singular perturbation of inverses and generalized inverses. It also offers original applications in Markov chains, Markov decision processes, optimization, and applications to Google PageRank? and the Hamiltonian cycle problem as well as input retrieval in linear control systems and a problem section in every chapter to aid in course preparation.
Download or read book Computational Methods in Structural Dynamics written by L. Meirovitch and published by Springer Science & Business Media. This book was released on 1980-10-31 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vibration Analysis of Rotors written by Chong-Won Lee and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended for use as an advanced course in either rotordynamics or vibration at the graduate level. This text has mostly grown out of the research work in my laboratory and the lectures given to graduate students in the Mechanical Engineering Department, KAIST. The text contains a variety of topics not normally found in rotordynamics or vibration textbooks. The text emphasizes the analytical aspects and is thus quite different from conventional rotordynamics texts; potential readers are expected to have a firm background in elementary rotordynamics and vibration. In most previously published rotordynamics texts, the behavior of simple rotors has been of a primary concern, while more realistic, multi-degree-f-freedom or continuous systems are seldom treated in a rigorous way, mostly due to the difficulty of a mathematical treatment of such complicated systems. When one wanted to gain a deep insight into dynamic phenomena of complicated rotor systems, one has, in the past, either had to rely on computational techniques, such as the transfer matrix and finite element methods, or cautiously to extend ideas learned from simple rotors whose analytical solutions are readily available. The former methods are limited in the interpretation of results, since the calculations relate only to the simulated case, not to more general system behavior. Ideas learned from simple rotors can, fortunately, often be extended to many practical rotor systems, but there is of course no guarantee of their validity.
Download or read book Structural Control written by U. Leipholz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of "structural control", which had already experienced some attention through publications, for example by Roorda, Yao, Yang, Abdel-Rohman, Leipholz etc. , mostly in journals of ASCE, was given its fIrst international forum at the University of Waterloo, Waterloo, Ontario, Canada, via an ruTMf - Symposium held in June, 1979. This very successful event gathered experts from a variety of technical and theoretical domains in which control plays tradi tionally an essential role and was meant to present the new idea of structural control to a broad audience, thus triggering interest and commitment as well as cross-fertilization. However, the peculiarities of structural control were already sumciently well pointed out and stressed by those participants of the symposium who had devoted themselves earlier to this specwc topic for some time. The result of presentations and discussions are collected in a set of Proceedings entitled "Structural Control", published by North - Holland Publishing Company and the Solid Mechanics Division (SMD) of the University of Waterloo. The stimulation following this fIrst symposium was quite noticeable in the literature and led to the conviction of many researchers that after a reasonable period of time, a second meeting should be held to collect the fruits produced by the intermediate efforts of those working with increased emphasis on structural control. Therefore, Professors J. T. P. Yao, Department of Civil Engineering, Purdue University and H. H. E.
Download or read book Modal Analysis and Testing written by Júlio M. Montalvão e Silva and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Sesimbra, Portugal, 3-15 May, 1998
Download or read book Surface Waves in Geomechanics Direct and Inverse Modelling for Soils and Rocks written by Carlo G. Lai and published by Springer Science & Business Media. This book was released on 2007-03-23 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theories of surface waves develop since the end of XIX century and many fundamental problems like existence, phase and group velocities, attenuation (quality factor), mode conversion, etc. have been, in part successfully, solved within the framework of such simple models as ideal fluids^ or linear elasticity. However, a sufficiently complete presentation of this subject, particularly for solids, is still missing in the literature. The sole exception is the book of I. A. Viktorov^ which contains an extensive discussion of fundamental properties of surface waves in homogeneous and stratified linear elastic solids with particular emphasis on contributions of Russian scientists. Unfortunately, the book has never been translated to English and its Russian version is also hardly available. Practical applications of surface waves develop intensively since a much shorter period of time than theories even though the motivation of discoverers of surface waves such as Lord Rayleigh stems from their appearance in geophysics and seismology. Nowadays the growing interest in practical applications of surface waves stem from the following two main factors: surface waves are ideal for developing relatively cheap and convenient methods of nondestructive testing of various systems spanning from nanomaterials (e.g.
Download or read book Templates for the Solution of Algebraic Eigenvalue Problems written by Zhaojun Bai and published by SIAM. This book was released on 2000-01-01 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. Using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem.
Download or read book Computational Techniques for Structural Health Monitoring written by Srinivasan Gopalakrishnan and published by Springer Science & Business Media. This book was released on 2011-08-01 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increased level of activity on structural health monitoring (SHM) in various universities and research labs has resulted in the development of new methodologies for both identifying the existing damage in structures and predicting the onset of damage that may occur during service. Designers often have to consult a variety of textbooks, journal papers and reports, because many of these methodologies require advanced knowledge of mechanics, dynamics, wave propagation, and material science. Computational Techniques for Structural Health Monitoring gives a one-volume, in-depth introduction to the different computational methodologies available for rapid detection of flaws in structures. Techniques, algorithms and results are presented in a way that allows their direct application. A number of case studies are included to highlight further the practical aspects of the selected topics. Computational Techniques for Structural Health Monitoring also provides the reader with numerical simulation tools that are essential to the development of novel algorithms for the interpretation of experimental measurements, and for the identification of damage and its characterization. Upon reading Computational Techniques for Structural Health Monitoring, graduate students will be able to begin research-level work in the area of structural health monitoring. The level of detail in the description of formulation and implementation also allows engineers to apply the concepts directly in their research.
Download or read book Vibration Analysis written by Rao V. Dukkipati and published by Alpha Science Int'l Ltd.. This book was released on 2004 with total page 1022 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses in a concise but through manner fundamental statement of the theory, principles and methods of mechanical vibrations.
Download or read book Nonconservative Stability Problems of Modern Physics written by Oleg N. Kirillov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-03-08 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This updated revision gives a complete and topical overview on Nonconservative Stability which is essential for many areas of science and technology ranging from particles trapping in optical tweezers and dynamics of subcellular structures to dissipative and radiative instabilities in fluid mechanics, astrophysics and celestial mechanics. The author presents relevant mathematical concepts as well as rigorous stability results and numerous classical and contemporary examples from non-conservative mechanics and non-Hermitian physics. New coverage of ponderomotive magnetism, experimental detection of Ziegler’s destabilization phenomenon and theory of double-diffusive instabilities in magnetohydrodynamics.
Download or read book Scalar Vector and Matrix Mathematics written by Dennis S. Bernstein and published by Princeton University Press. This book was released on 2018-02-27 with total page 1594 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index
