Vibration of Mechanical Systems
This is a textbook for a ﬁrst course in mechanical vibrations. There are many books in this area that try to include everything, thus they have become exhaustive compendiums that are overwhelming for an undergraduate. In this book, all the basic concepts in mechanical vibrations are clearly identiﬁed and presented in aconcise and simple manner with illustrative and practical examples. Vibration concepts include a review of selected topics in mechanics; a description of single-degree-of-freedom (SDOF) systems in terms of equivalent mass, equivalent stiffness, and equivalent damping; a uniﬁed treatment of various forced response problems (base excitation and rotating balance); an introduction to systems thinking,highlighting the fact that SDOF analysis is a building block for multi-degree-of-freedom (MDOF) and continuous system analyses via modal analysis; and a simple introduction to ﬁnite element analysis to connect continuous system and MDOF analyses. There are more than 60 exercise problems and a complete solutions manual. The use of MATLAB R software is emphasized. Alok Sinha is a Professor of MechanicalEngineering at The Pennsylvania State University (PSU), University Park. He received his PhD degree in mechanical engineering from Carnegie Mellon University. He has been a PSU faculty member since August 1983. His areas of teaching and research are vibration, control systems, jet engines, robotics, neural networks, and nanotechnology. He is the author of Linear Systems: Optimal and RobustControl. He has served as a Visiting Associate Professor of Aeronautics and Astronautics at MIT, Cambridge, MA, and as a researcher at Pratt & Whitney, East Hartford, CT. He has also been an associate editor of ASME Journal of Dynamic Systems, Measurement, and Control. At present, he serves as an associate editor of ASME Journal of Turbomachinery and AIAA Journal. Alok Sinha is a Fellow of ASME. He hasreceived the NASA certiﬁcate of recognition for signiﬁcant contributions to the Space Shuttle Microgravity Mission.
VIBRATION OF MECHANICAL SYSTEMS
The Pennsylvania State University
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU,UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521518734 © Alok Sinha 2010 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of CambridgeUniversity Press. First published in print format 2010 ISBN-13 ISBN-13 978-0-511-77527-7 978-0-521-51873-4 eBook (EBL) Hardback
Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.To My Wife Hansa and My Daughters Divya and Swarna
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1 Equivalent Single-Degree-of-Freedom System and Free Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Degrees of Freedom 1.2 Elements of a Vibratory System 1.2.1 Mass and/orMass-Moment of Inertia Pure Translational Motion Pure Rotational Motion Planar Motion (Combined Rotation and Translation) of a Rigid Body Special Case: Pure Rotation about a Fixed Point 1.2.2 Spring Pure Translational Motion Pure Rotational Motion 1.2.3 Damper Pure Translational Motion Pure Rotational Motion 1.3 Equivalent Mass, Equivalent Stiffness, and Equivalent Damping Constant for an SDOF...