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| mechanical and electrical vibrations differential equations: Differential Equations with Applications Paul D. Ritger, Nicholas J. Rose, 2000-01-01 Coherent, balanced introductory text focuses on initial- and boundary-value problems, general properties of linear equations, and the differences between linear and nonlinear systems. Includes large number of illustrative examples worked out in detail and extensive sets of problems. Answers or hints to most problems appear at end. |
| mechanical and electrical vibrations differential equations: Differential Equations James R. Brannan, William E. Boyce, 2015-02-17 The modern landscape of technology and industry demands an equally modern approach to differential equations in the classroom. Designed for a first course in differential equations, the third edition of Brannan/Boyce’s Differential Equations: An Introduction to Modern Methods and Applications Binder Ready Version is consistent with the way engineers and scientists use mathematics in their daily work. The text emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. The focus on fundamental skills, careful application of technology, and practice in modeling complex systems prepares students for the realities of the new millennium, providing the building blocks to be successful problem-solvers in today’s workplace. This text is an unbound, binder-ready version. |
| mechanical and electrical vibrations differential equations: Elementary Differential Equations and Boundary Value Problems William E. Boyce, Richard C. DiPrima, Douglas B. Meade, 2017-08-21 Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. |
| mechanical and electrical vibrations differential equations: Mechanical Vibration Haym Benaroya, 2004-10-13 An effective text must be well balanced and thorough in its approach to a topic as expansive as vibration, and Mechanical Vibration is just such a textbook. Written for both senior undergraduate and graduate course levels, this updated and expanded second edition integrates uncertainty and control into the discussion of vibration, outlining basic concepts before delving into the mathematical rigors of modeling and analysis. Mechanical Vibration: Analysis, Uncertainties, and Control, Second Edition provides example problems, end-of-chapter exercises, and an up-to-date set of mini-projects to enhance students' computational abilities and includes abundant references for further study or more in-depth information. The author provides a MATLAB® primer on an accompanying CD-ROM, which contains original programs that can be used to solve complex problems and test solutions. The book is self-contained, covering both basic and more advanced topics such as stochastic processes and variational approaches. It concludes with a completely new chapter on nonlinear vibration and stability. Professors will find that the logical sequence of material is ideal for tailoring individualized syllabi, and students will benefit from the abundance of problems and MATLAB programs provided in the text and on the accompanying CD-ROM, respectively. A solutions manual is also available with qualifying course adoptions. |
| mechanical and electrical vibrations differential equations: Mechanical and Electrical Vibrations John Robert Barker, 1964 |
| mechanical and electrical vibrations differential equations: Notes on Diffy Qs Jiri Lebl, 2019-11-13 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. |
| mechanical and electrical vibrations differential equations: Simultaneous Systems of Differential Equations and Multi-Dimensional Vibrations Luis Manuel Braga da Costa Campos, 2019-11-05 Simultaneous Differential Equations and Multi-Dimensional Vibrations is the fourth book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This fourth book consists of two chapters (chapters 7 and 8 of the set). The first chapter concerns simultaneous systems of ordinary differential equations and focuses mostly on the cases that have a matrix of characteristic polynomials, namely linear systems with constant or homogeneous power coefficients. The method of the matrix of characteristic polynomials also applies to simultaneous systems of linear finite difference equations with constant coefficients. The second chapter considers linear multi-dimensional oscillators with any number of degrees of freedom including damping, forcing, and multiple resonance. The discrete oscillators may be extended from a finite number of degrees-of-freedom to infinite chains. The continuous oscillators correspond to waves in homogeneous or inhomogeneous media, including elastic, acoustic, electromagnetic, and water surface waves. The combination of propagation and dissipation leads to the equations of mathematical physics. Presents simultaneous systems of ordinary differential equations and their elimination for a single ordinary differential equation Includes cases with a matrix of characteristic polynomials, including simultaneous systems of linear differential and finite difference equations with constant coefficients Covers multi-dimensional oscillators with damping and forcing, including modal decomposition, natural frequencies and coordinates, and multiple resonance Discusses waves in inhomogeneous media, such as elastic, electromagnetic, acoustic, and water waves Includes solutions of partial differential equations of mathematical physics by separation of variables leading to ordinary differential equations |
| mechanical and electrical vibrations differential equations: Elementary Differential Equations William E. Boyce, Richard C. DiPrima, Douglas B. Meade, 2017-08-14 With Wiley's Enhanced E-Text, you get all the benefits of a downloadable, reflowable eBook with added resources to make your study time more effective, including: Embedded & searchable equations, figures & tables Math XML Index with linked pages numbers for easy reference Redrawn full color figures to allow for easier identification Elementary Differential Equations, 11th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two ] or three ] semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. |
| mechanical and electrical vibrations differential equations: Engineering Differential Equations Bill Goodwine, 2010-11-11 This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra. |
| mechanical and electrical vibrations differential equations: Ordinary Differential Equations and Mechanical Systems Jan Awrejcewicz, 2014-09-17 This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization. Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition. The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering. |
| mechanical and electrical vibrations differential equations: An Elementary Treatise on Differential Equations and Their Applications Henry Thomas Herbert Piaggio, 1921 |
| mechanical and electrical vibrations differential equations: Mechanical Vibrations J. P. Den Hartog, 2011-03-23 This book grew from a course of lectures given to students in the Design School of the Westinghouse Company in Pittsburgh, Pa., in the period from 1926 to 1932, when the subject had not yet been introduced into the curriculum of our technical schools. From 1932 until the beginning of the war, it became a regular course at the Harvard Engineering School, and the book was written for the purpose of facilitating that course, being first published in 1934. In its first edition, it was influenced entirely by the author’s industrial experience at Westinghouse; the later editions have brought modifications and additions suggested by actual problems published in the literature, by private consulting practice, and by service during the war in the Bureau of Ships of the U.S. Navy. The book aims to be as simple as is compatible with a reasonably complete treatment of the subject. Mathematics has not been avoided, but in all cases the mathematical approach used is the simplest one available. In the third edition the number of problems has again been increased, while the principal changes in the text concern subjects in which recent advances have been made, such as airplane wing flutter, helicopter ground vibration, torsional pendulum dampers, singing ships’ propellers, and electronic instruments. |
| mechanical and electrical vibrations differential equations: Mechanical Vibrations Yvon Mori, 2017-01-18 The purpose of this book is to clarify the issues related to the environment of mechanical vibrations in the material life profile. In particular, through their simulation testing laboratory, through a better understanding of the physical phenomenon, means to implement to simulate, measurements and interpretations associated results. It is aimed at development of technical consultants, quality and services primarily to those testing laboratories, as well as to all those who are faced with supply reference to the environmental test calls and particularly here, vibration tests. Furthermore it should also interest students of engineering schools in the areas of competence of their future professions affected by vibration. |
| mechanical and electrical vibrations differential equations: Nonlinear Vibrations in Mechanical and Electrical Systems J. J. Stoker, 1992-01-24 Presents underlying principles and theories using an easily understood approach. Focuses specifically on those features of the problems in which nonlinearity results in a variety of distinctive new phenomena that can be treated by techniques both interesting and instructive in themselves and which do not require the use of sophisticated mathematics. Recent work discussed includes the endeavors of Levinson and Smith on the existence and uniqueness of the periodic solution in a general case of the self-excited type, Haag and Dorodnitsyn on asymptotic developments and quantities associated with relaxation oscillations. Along with 5 appendices containing rigorous existence and uniqueness proofs, readers are both implicitly and explicitly supplied with hints regarding new problems to be tackled plus numerous ideas and techniques that can be used to solve them. |
| mechanical and electrical vibrations differential equations: System Dynamics and Mechanical Vibrations Dietmar Findeisen, 2013-03-09 The Aim ofthe Book. This book is concerned with the subjects of vibrations and system dynamics on an integrated basis. Design engineers find themselves confronted with demands made on machin ery, structures and dynamic systems which are increasing at such a rate that dy namic performance requirements are always rising. Hence, advances in analysis and design techniques have to keep pace with recent developments in strong lightweight materials, more extensive knowledge of materials properties and structural loading. Whereas the excitation applied to structures is always increas ing, the machine mass and damping is reduced. Consequently, unwanted vibra tions can have very serious effects on dynamic systems. It is, therefore, essential to carry out vibration analysis as an inherent part of machine design. The problems arising either from the observed or predicted dynamic behaviour of systems are of particular interest in control theory. Vibration theory places emphasis on analysis, which implies determining the response to given excita tions, and any design amounts to changing the system parameters so as to bring about a satisfactory response. The improvement in performance achieved by changing solely the parameters of the mechanical system is very limited. How ever, a new approach to system design has proved to be more successful. It con sists of designing forces that, when exerted on the system, produce a satisfactory response. This approach, known as control, has become a ubiquitous part of the engineering curriculum, completing the conventional mechanical disciplines. |
| mechanical and electrical vibrations differential equations: Electrical Vibration Instruments Arthur Edwin Kennelly, 1923 |
| mechanical and electrical vibrations differential equations: Advanced Vibration Analysis S. Graham Kelly, 2006-12-19 Delineating a comprehensive theory, Advanced Vibration Analysis provides the bedrock for building a general mathematical framework for the analysis of a model of a physical system undergoing vibration. The book illustrates how the physics of a problem is used to develop a more specific framework for the analysis of that problem. The author elucidates a general theory applicable to both discrete and continuous systems and includes proofs of important results, especially proofs that are themselves instructive for a thorough understanding of the result. The book begins with a discussion of the physics of dynamic systems comprised of particles, rigid bodies, and deformable bodies and the physics and mathematics for the analysis of a system with a single-degree-of-freedom. It develops mathematical models using energy methods and presents the mathematical foundation for the framework. The author illustrates the development and analysis of linear operators used in various problems and the formulation of the differential equations governing the response of a conservative linear system in terms of self-adjoint linear operators, the inertia operator, and the stiffness operator. The author focuses on the free response of linear conservative systems and the free response of non-self-adjoint systems. He explores three method for determining the forced response and approximate methods of solution for continuous systems. The use of the mathematical foundation and the application of the physics to build a framework for the modeling and development of the response is emphasized throughout the book. The presence of the framework becomes more important as the complexity of the system increases. The text builds the foundation, formalizes it, and uses it in a consistent fashion including application to contemporary research using linear vibrations. |
| mechanical and electrical vibrations differential equations: Mechanical Vibrations Singiresu S. Rao, 2017 For courses in vibration engineering. Building Knowledge: Concepts of Vibration in Engineering Retaining the style of previous editions, this Sixth Edition of Mechanical Vibrations effectively presents theory, computational aspects, and applications of vibration, introducing undergraduate engineering students to the subject of vibration engineering in as simple a manner as possible. Emphasizing computer techniques of analysis, Mechanical Vibrations thoroughly explains the fundamentals of vibration analysis, building on the understanding achieved by students in previous undergraduate mechanics courses. Related concepts are discussed, and real-life applications, examples, problems, and illustrations related to vibration analysis enhance comprehension of all concepts and material. In the Sixth Edition, several additions and revisions have been made--including new examples, problems, and illustrations--with the goal of making coverage of concepts both more comprehensive and easier to follow. |
| mechanical and electrical vibrations differential equations: Partial Differential Equations Walter A. Strauss, 2007-12-21 Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics. |
| mechanical and electrical vibrations differential equations: A Course in Differential Equations with Boundary Value Problems Stephen A. Wirkus, Randall J. Swift, Ryan Szypowski, 2017-01-24 A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author’s successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student’s field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged. The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra. Most significantly, computer labs are given in MATLAB®, Mathematica®, and MapleTM. The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included. Features MATLAB®, Mathematica®, and MapleTM are incorporated at the end of each chapter All three software packages have parallel code and exercises There are numerous problems of varying difficulty for both the applied and pure math major, as well as problems for engineering, physical science and other students. An appendix that gives the reader a crash course in the three software packages Chapter reviews at the end of each chapter to help the students review Projects at the end of each chapter that go into detail about certain topics and introduce new topics that the students are now ready to see Answers to most of the odd problems in the back of the book |
| mechanical and electrical vibrations differential equations: Vibrations and Audible Noise in Alternating Current Machines R. Belmans, K.J. Binns, W. Geysen, A. Vandenput, 2012-12-06 Proceedings of the NATO Advanced Research Workshop on Mechanical Vibrations and Audible Noise in Alternating Current Machines, Leuven, Belgium, August 4-8, 1986 |
| mechanical and electrical vibrations differential equations: Applied Structural and Mechanical Vibrations Paolo L. Gatti, 2014-02-24 The second edition of Applied Structural and Mechanical Vibrations: Theory and Methods continues the first edition’s dual focus on the mathematical theory and the practical aspects of engineering vibrations measurement and analysis. This book emphasises the physical concepts, brings together theory and practice, and includes a number of worked-out examples of varying difficulty and an extensive list of references. What’s New in the Second Edition: Adds new material on response spectra Includes revised chapters on modal analysis and on probability and statistics Introduces new material on stochastic processes and random vibrations The book explores the theory and methods of engineering vibrations. By also addressing the measurement and analysis of vibrations in real-world applications, it provides and explains the fundamental concepts that form the common background of disciplines such as structural dynamics, mechanical, aerospace, automotive, earthquake, and civil engineering. Applied Structural and Mechanical Vibrations: Theory and Methods presents the material in order of increasing complexity. It introduces the simplest physical systems capable of vibratory motion in the fundamental chapters, and then moves on to a detailed study of the free and forced vibration response of more complex systems. It also explains some of the most important approximate methods and experimental techniques used to model and analyze these systems. With respect to the first edition, all the material has been revised and updated, making it a superb reference for advanced students and professionals working in the field. |
| mechanical and electrical vibrations differential equations: Asymptotic Behavior and Stability Problems in Ordinary Differential Equations Lamberto Cesari, 2013-11-09 In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call qualitative theory of differential equations. The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications. |
| mechanical and electrical vibrations differential equations: The Shock and Vibration Bulletin , 1978 |
| mechanical and electrical vibrations differential equations: Active Control of Vibration Christopher C. Fuller, Sharon Elliott, P. A. Nelson, 1996-02-08 This book is a companion text to Active Control of Sound by P.A. Nelson and S.J. Elliott, also published by Academic Press. It summarizes the principles underlying active vibration control and its practical applications by combining material from vibrations, mechanics, signal processing, acoustics, and control theory. The emphasis of the book is on the active control of waves in structures, the active isolation of vibrations, the use of distributed strain actuators and sensors, and the active control of structurally radiated sound. The feedforward control of deterministic disturbances, the active control of structural waves and the active isolation of vibrations are covered in detail, as well as the more conventional work on modal feedback. The principles of the transducers used as actuateors and sensors for such control strategies are also given an in-depth description. The reader will find particularly interesting the two chapters on the active control of sound radiation from structures: active structural acoustic control. The reason for controlling high frequency vibration is often to prevent sound radiation, and the principles and practical application of such techniques are presented here for both plates and cylinders. The volume is written in textbook style and is aimed at students, practicing engineers, and researchers. - Combines material from vibrations, signal processing, mechanics, and controls - Summarizes new research in the field |
| mechanical and electrical vibrations differential equations: Torsional Vibration of Turbo-Machinery Duncan Walker, 2003-11-21 Vibration, excessive noise and other dynamics-related problems that limit or prevent operation are a major manufacturing concern in airplanes, auto crankshafts, home appliances, etc. This detailed monograph provides in-depth coverage of state-of-the-art vibration analysis techniques used to prevent design and operational malfunction. * Torsional vibration mathematical modeling * Forced response analysis * Vibration measurement methods and monitoring * Application case studies * SI units used throughout |
| mechanical and electrical vibrations differential equations: Transactions of the American Institute of Electrical Engineers , 1917 |
| mechanical and electrical vibrations differential equations: Calcutta Review , 1921 |
| mechanical and electrical vibrations differential equations: Devices for Damping Mechanical Vibrations Mildred Benton, 1956 |
| mechanical and electrical vibrations differential equations: Shock & Vibration, Aircraft/Aerospace, Energy Harvesting, Acoustics & Optics, Volume 9 Julie M. Harvie, Javad Baqersad, 2017-04-17 Shock & Vibration, Aircraft/Aerospace and Energy Harvesting, Volume 9: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the ninth volume of ten 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 Shock & Vibration, Aircraft/Aerospace and Energy Harvesting including papers on: Shock & Vibration Testing Aircraft/Aerospace Applications Optical Techniques: Digital Image Correlation Vibration Suppression & Control Damage Detection Energy Harvesting |
| mechanical and electrical vibrations differential equations: Applied Mechanics Reviews , 1971 |
| mechanical and electrical vibrations differential equations: Fundamentals of Mechanical Vibrations Liang-Wu Cai, 2016-06-13 This introductory book covers the most fundamental aspects of linear vibration analysis for mechanical engineering students and engineers. Consisting of five major topics, each has its own chapter and is aligned with five major objectives of the book. It starts from a concise, rigorous and yet accessible introduction to Lagrangian dynamics as a tool for obtaining the governing equation(s) for a system, the starting point of vibration analysis. The second topic introduces mathematical tools for vibration analyses for single degree-of-freedom systems. In the process, every example includes a section Exploring the Solution with MATLAB. This is intended to develop student's affinity to symbolic calculations, and to encourage curiosity-driven explorations. The third topic introduces the lumped-parameter modeling to convert simple engineering structures into models of equivalent masses and springs. The fourth topic introduces mathematical tools for general multiple degrees of freedom systems, with many examples suitable for hand calculation, and a few computer-aided examples that bridges the lumped-parameter models and continuous systems. The last topic introduces the finite element method as a jumping point for students to understand the theory and the use of commercial software for vibration analysis of real-world structures. |
| mechanical and electrical vibrations differential equations: The Shock and Vibration Digest , 1984 |
| mechanical and electrical vibrations differential equations: Applied Structural and Mechanical Vibrations Paolo L. Gatti, 1999-09-23 The fundamental concepts, ideas and methods underlying all vibration phenomena are explained and illustrated in this book. The principles of classical linear vibration theory are brought together with vibration measurement, signal processing and random vibration for application to vibration problems in all areas of engineering. The book pays partic |
| mechanical and electrical vibrations differential equations: U.S. Government Research Reports , 1963 |
| mechanical and electrical vibrations differential equations: New York Review of the Telegraph and Telephone and Electrical Journal , 1887 |
| mechanical and electrical vibrations differential equations: Power Ultrasonics Juan A. Gallego-Juarez, Karl F. Graff, Margaret Lucas, 2023-04-06 Power Ultrasonics: Applications of High-Intensity Ultrasound, Second Edition provides a comprehensive reference on the fundamentals, processing, engineering, medical, food and pharmaceutical applications of ultrasonic processing. Chapters cover the fundamentals of nonlinear propagation of ultrasonic waves in fluids and solids, discuss the materials and designs of power ultrasonic transducers and devices, identify applications of high power ultrasound in materials engineering and mechanical engineering, food processing technology, environmental monitoring and remediation and industrial and chemical processing (including pharmaceuticals), medicine and biotechnology, and cover developments in ultrasound therapy and surgery applications.The new edition also includes recent advances in modeling, characterization and measurement techniques, along with additive manufacturing and micromanufacturing. This is an invaluable reference for graduate students and researchers working in the disciplines of materials science and engineering. In addition, those working on the physics of acoustics, sound and ultrasound, sonochemistry, acoustic engineering and industrial process technology, R&D managers, production, and biomedical engineers will find it useful to their work. - Covers the fundamentals of nonlinear propagation of ultrasonic waves in fluids and solids - Discusses the materials and designs of power ultrasonic transducers and devices - Considers state-of-the-art power sonic applications across a wide range of industries |
| mechanical and electrical vibrations differential equations: General Catalog University of California, Los Angeles, 1965 |
| mechanical and electrical vibrations differential equations: Vibrations of Shells and Rods Khanh C. Le, 2012-12-06 We live in a world of vibrations and waves, without which there would not be sound, light, radio, television, communication etc. That is why the study of vibrations and waves is so important in many branches of physics and me chanics. This book is devoted to the study of small mechanical vibrations of shells and rods, which are made of elastic or piezoelectric materials. But even in this very special field there are already many excellent books and mono graphs written since the monumental work by Rayleigh [47]. The peculiarity of the present book is that we regard the equations of shells and rods as two- and one-dimensional approximate equations which can be derived from the three-dimensional theory by using the variational-asymptotic method. The latter has been invented especially for those variational problems which contain small parameters. It turns out that for vibrations of shells and rods there are many situations in which such small parameters exist. Thus, the application of the variational-asymptotic method enables one to derive not only the classical two- and one-dimensional theories of low-frequency vibra tions of shells and rods, but also the theories of high-frequency (or thickness) vibrations. |
| mechanical and electrical vibrations differential equations: Geophysical Abstracts ... , 1954 |
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