Vibrations and Waves in Continuous Mechanical Systems

Vibrations and Waves in Continuous Mechanical Systems PDF

Author: Peter Hagedorn

Publisher: John Wiley & Sons

Published: 2007-10-22

Total Pages: 396

ISBN-13: 9780470518427

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The subject of vibrations is of fundamental importance in engineering and technology. Discrete modelling is sufficient to understand the dynamics of many vibrating systems; however a large number of vibration phenomena are far more easily understood when modelled as continuous systems. The theory of vibrations in continuous systems is crucial to the understanding of engineering problems in areas as diverse as automotive brakes, overhead transmission lines, liquid filled tanks, ultrasonic testing or room acoustics. Starting from an elementary level, Vibrations and Waves in Continuous Mechanical Systems helps develop a comprehensive understanding of the theory of these systems and the tools with which to analyse them, before progressing to more advanced topics. Presents dynamics and analysis techniques for a wide range of continuous systems including strings, bars, beams, membranes, plates, fluids and elastic bodies in one, two and three dimensions. Covers special topics such as the interaction of discrete and continuous systems, vibrations in translating media, and sound emission from vibrating surfaces, among others. Develops the reader’s understanding by progressing from very simple results to more complex analysis without skipping the key steps in the derivations. Offers a number of new topics and exercises that form essential steppingstones to the present level of research in the field. Includes exercises at the end of the chapters based on both the academic and practical experience of the authors. Vibrations and Waves in Continuous Mechanical Systems provides a first course on the vibrations of continuous systems that will be suitable for students of continuous system dynamics, at senior undergraduate and graduate levels, in mechanical, civil and aerospace engineering. It will also appeal to researchers developing theory and analysis within the field.

Isospectral Vibrating Systems

Isospectral Vibrating Systems PDF

Author: Ranjan Ganguli

Publisher: CRC Press

Published: 2021-08-10

Total Pages: 303

ISBN-13: 1000413462

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This book presents an isospectral approach for several important mechanical vibrating systems. Discrete and continuous isospectral systems are discussed using a simple multi-degree of freedom spring-mass system followed by illustration of isospectral beams and their solution through evolutionary computing. Next, it addresses axially loaded Euler-Bernoulli beams and aims to find isospectral counterparts of these systems. The practical application of these isospectral systems for vibration testing and for finding new closed form solutions is discussed. A considerable part of the book is devoted to isospectral rotating beams and their non-rotating analogs including Rayleigh beams. Aimed at researchers and graduate students in mechanical; aerospace; civil; automotive; ocean engineering especially mechanical vibrations, this monograph: Discusses isospectral vibrating systems to aid vibration testing and computational analysis Explores isospectral analogs between rotating and non-rotating structures Provides simpler isospectral beams for vibration testing and for 3D printing Uses firefly optimization method and electromagnetism inspired optimization method to find isospectral systems Shows the use of isospectral systems to find new closed form solutions using an indirect approach

Lambda-Matrices and Vibrating Systems

Lambda-Matrices and Vibrating Systems PDF

Author: Peter Lancaster

Publisher: Courier Corporation

Published: 2011-11-30

Total Pages: 226

ISBN-13: 0486153266

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Features aspects and solutions of problems of linear vibrating systems with a finite number of degrees of freedom. Starts with development of necessary tools in matrix theory, followed by numerical procedures for relevant matrix formulations and relevant theory of differential equations. Minimum of mathematical abstraction; assumes a familiarity with matrix theory, elementary calculus. 1966 edition.

Lambda-Matrices and Vibrating Systems

Lambda-Matrices and Vibrating Systems PDF

Author: Peter Lancaster

Publisher: Elsevier

Published: 2014-07-10

Total Pages: 211

ISBN-13: 1483150968

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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.

The Behaviour of Nonlinear Vibrating Systems

The Behaviour of Nonlinear Vibrating Systems PDF

Author: Wanda Szemplinska

Publisher: Springer Science & Business Media

Published: 1990-06-30

Total Pages: 370

ISBN-13: 9780792303695

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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.

Real-Time Structural Health Monitoring of Vibrating Systems

Real-Time Structural Health Monitoring of Vibrating Systems PDF

Author: Basuraj Bhowmik

Publisher: CRC Press

Published: 2022-09-22

Total Pages: 249

ISBN-13: 1000706052

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Targeted at researchers and practitioners in the field of science and engineering, the book provides an introduction to real time structural health monitoring. Most work to date is based on algorithms that require windowing of the accumulated data, this work presents a coherent transition from the traditional batch mode practice to a recently developed array of recursive approaches. The book mainly focuses on the theoretical development and engineering applications of algorithms that are based on first order perturbation (FOP) techniques. The development of real time algorithms aimed at identifying the structural systems and the inflicted damage, online, through theoretical approaches paves the way for an in-depth understanding of the discussed topics. It then continues to demonstrate the solution to a class of inverse dynamic problems through numerically simulated systems. Extensive theoretical derivations supported by mathematical formulations, pivoted around the simple concepts of eigenspace updates, forms the key cornerstone of the book. The output response streaming in real time from multi degree of freedom systems provide key information about the system’s health that is subsequently utilized to identify the modal parameters and the damage, in real time. Damage indicators connotative of the nature, instant and location of damage, identified in a single framework are developed in the light of real time damage case studies. Backed by a comprehensive assortment of experimental test-beds, this book includes demonstrations to emulate real life damage scenarios under controlled laboratory conditions. Applicability of the proposed recursive methods towards practical problems demonstrate their robustness as viable candidates for real time structural health monitoring.

System Dynamics and Mechanical Vibrations

System Dynamics and Mechanical Vibrations PDF

Author: Dietmar Findeisen

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 399

ISBN-13: 3662042053

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A comprehensive treatment of "linear systems analysis" applied to dynamic systems as an approach to interdisciplinary system design beyond the related area of electrical engineering. The text gives an interpretation of mechanical vibrations based on the theory of dynamic systems, aiming to bridge the gap between existing theoretical methods in different engineering disciplines and to enable advanced students or professionals to model dynamic and vibrating systems with reference to communication and control processes. Emphasizing the theory it presents a balanced coverage of analytical principles and applications to vibrations with regard to mechatronic problems.

Vibration Theory and Applications with Finite Elements and Active Vibration Control

Vibration Theory and Applications with Finite Elements and Active Vibration Control PDF

Author: Alan Palazzolo

Publisher: John Wiley & Sons

Published: 2016-01-11

Total Pages: 973

ISBN-13: 1118404262

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Based on many years of research and teaching, this book brings together all the important topics in linear vibration theory, including failure models, kinematics and modeling, unstable vibrating systems, rotordynamics, model reduction methods, and finite element methods utilizing truss, beam, membrane and solid elements. It also explores in detail active vibration control, instability and modal analysis. The book provides the modeling skills and knowledge required for modern engineering practice, plus the tools needed to identify, formulate and solve engineering problems effectively.

Vibration Control For Optomechanical Systems

Vibration Control For Optomechanical Systems PDF

Author: Vyacheslav M Ryaboy

Publisher: World Scientific

Published: 2021-11-29

Total Pages: 280

ISBN-13: 9811237352

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Vibration presents a major challenge to advanced experiments and technological processes in engineering, physics and life sciences that rely on optics and optoelectronics. This compendium discusses ways in which vibration may affect optical performance and describes methods and means of reducing this impact. Principal methods of vibration control, namely, damping and isolation are highlighted using mathematical models and real-life examples.The unique text covers some topics that are important for optomechanical applications but are lacking in general vibration texts, such as dynamics and stability of elastically supported systems with high centers of gravity, physics of pneumatic isolators, and application of dynamic absorbers to vibration-isolated systems.This useful reference book enables the reader to apply the vibration control tools properly and perform basic analytical and experimental tasks of estimating and verifying their performance. It is also a must-have textbook for undergraduate or graduate-level courses in vibration control and optomechanics.Related Link(s)