Dynamics Formulas and Problems

Transcription

1 Dynamics Formulas and Problems

2 Dietmar Gross Wolfgang Ehlers Peter Wriggers Jörg Schröder Ralf Müller Dynamics Formulas and Problems Engineering Mechanics 3 123

3 Dietmar Gross Division of Solid Mechanics TU Darmstadt Darmstadt Wolfgang Ehlers Institute of Applied Mechanics Universität Stuttgart Stuttgart Jörg Schröder Institute of Mechanics Universität Duisburg-Essen Essen Ralf Müller Engineering Mechanics TU Kaiserslautern Kaiserslautern Peter Wriggers Institute of Continuum Mechanics Leibniz Universität Hannover Hannover ISBN ISBN (ebook) DOI / Library of Congress Control Number: Springer-Verlag Berlin Heidelberg 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer-Verlag GmbH The registered company address is: Heidelberger Platz 3, Berlin,

4 Preface This 3 rd volume of the Formulas and Problems concludes the series to the basic courses in Engineering Mechanics. Experience shows that the field of Dynamics is particularly difficult for students, because besides the concept of force now additional kinematic quantities occur, which must be brought into relation with each other and with the forces. Therefore, with numerous purely kinematical problems, we tried to deepen the understanding of the relevant geometric quantities and their description in different coordinate systems. Likewise, only by exercises, i.e. by an independent treatment of problems, one can gain experience, which basic principle leads to the solution in the simplest way. Often there are several approaches possible. Therefore we demonstrate this frequently so that the reader can realize the advantages and disadvantages of the alternatives. As in the 1 st and 2 nd volume, we deliberately placed the emphasis on the principal way how to to apply the theory and not in numerical results. The correct formulation of the relevant basic equations and their solution is in the beginning much more important than numerical calculations without a deeper understanding of the background. Experience also shows that it is an illusion to believe that simply reading and trying to comprehend the presented solutions leads to an understanding of the theory. Neither does it improve the problem solving skills. Therefore, we strongly recommend that the reader first tries to solve the problems independently, possibly by using other approaches. Let us emphasize that a collection of formulas and examples is only an additional aid when studying mechanics and it cannot replace a textbook. When the reader is not familiar with one or the other formula or concept, it is necessary to brush up the theory with the help of a textbook; a number of titles can be found in the list of references. Darmstadt, Stuttgart, Hannover, Essen and Kaiserslautern, Summer 2016 D. Gross W. Ehlers P. Wriggers J. Schröder R. Müller

5 Table of Contents Literature, Notation... IX 1 Kinematics of a Point Kinetics of a Point Mass Dynamics of a System of Point Masses Kinematics of Rigid Bodies Kinetics of a Rigid Body Impact Vibrations Non-Inertial Reference Frames Principles of Mechanics Hydrodynamics

6 Literature Textbooks Gross, D., Hauger, W., Schröder, J., Wall, W., Govindjee, S., Engineering Mechanics 3, Dynamics, 2nd edition, Springer 2014 Gross, D., Hauger, W., Wriggers, P., Technische Mechanik, vol 4: Hydromechanics, Elements of Avanced Mechanics, Numerical Methods (in German), 9th edition, Springer 2014 Beatty, M.F., Principles of Engineering Mechanics, vol 2: Dynamics, Springer 2005 Beer, F., Johnston, E.R., Cornwell, P., Vector Mechanics for Engineers: Dynamics, 10th edition, McGraw-Hill Education 2012 Hibbeler, R.C., Engineering Mechanics: Dynamics, 14th edition. Pearson 2016 Meriam, J.L., Kraige, L.G., Bolton, J.N., Engineering Mechanics: Dynamics, 8th edition, Wiley 2016 Plesha, M., Costanzo, F., Gray, G., Engineering Mechanics: Dynamics, 2nd edition, McGraw-Hill 2012 Pytel, A., Kiusalaas, J., Engineering Mechanics: Dynamics, 4th edition, Cengage Learning 2016 Shames, I.H., Engineering Mechanics: Dynamics, 4th edition, Pearson 1996 Collection of Problems Beer, F., Johnston, E.R., Cornwell, P., Vector Mechanics for Engineers: Dynamics, 10th edition, Solution Manual, McGraw-Hill 2012 Nelson, E.W., et al. Engineering Mechanics - Dynamics, 765 fully solved problems, Schaum s Outlines, McGraw-Hill Education 2010 Gray, G.L., Costanzo, F., Plesha, M.E., Solutions Manual, Engineering Mechanics: Dynamics, 1st edition, McGraw-Hill 2009 Hibbeler, R.C., Practice Problems Workbook, Engineering Mechanics: Dynamics, Pearson 2015 IX Notation In the problem solutions the following symbols are used: : abbreviation for equation of motion (impulse law) in direction of arrow. A : abbreviation for angular momentum theorem relative to point A with given positive rotation direction. abbreviation for it follows.