Carl Sisemore · Vít Babuška The Science and Engineering of Mechanical Shock The Science and Engineering of Mechanical Shock Carl Sisemore • Vít Babuška The Science and Engineering of Mechanical Shock 123 Carl Sisemore Vít Babuška Albuquerque, NM, USA Albuquerque, NM, USA This book describes objective technical material. Any subjective views or opinions that might be expressed are those of the authors and do not necessarily represent the views of Sandia National Laboratories, the US Department of Energy, or the US Government. ISBN 978-3-030-12102-0 ISBN 978-3-030-12103-7 (eBook) https://doi.org/10.1007/978-3-030-12103-7 Library of Congress Control Number: 2019933292 © Springer Nature Switzerland AG 2020 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland To Sara, Seth, Hosea, Josiah, and Hanna; Pavel and Tomáš; and the next generation of engineers. Preface Mechanical shock is often the misunderstood and neglected half of system envi- ronmental testing and analysis. Engineers design their systems to pass vibration exposure and hope that the systems pass shock testing. It has been said that the vibration laboratory is where components go for testing and the shock laboratory is where they go to die. The primary reason for this is that mechanical shock is generally not taught in either the undergraduate or graduate curriculum nor is it particularly straightforward. There are relatively few books dedicated to the study of mechanical shock, and most of those are engineering discipline-specific. While some undergraduate texts on vibrations may include a chapter on mechan- ical shock, thorough treatments of the topic are lacking. Nevertheless, shock is a mechanical environment that affects almost every device—from ships to spacecraft and from cell phones to shipping packages. Civil engineers worry about blast- induced shocks and earthquakes. Mechanical engineers are concerned with impact- induced shocks, while naval engineers must consider the effects of underwater explosive shocks on ships. Satellites must be robust to pyroshocks. The goal of this book is to bring together engineering information about mechan- ical shock from various disciplines into a cohesive text. The science of mechanical shock involves understanding of the basic physics of the event: how the dynamics of the system interplay with the high-speed transient nature of the excitation and the numerical methods for quantifying the shock event and its damage potential to various structures, systems, and components. The book includes information from naval and military applications, earthquake engineering, aerospace, and spacecraft in one reference. While the book is intended to provide basic information about the field of mechanical shock, the book and the topic are not themselves simplistic. It is assumed that the reader has a firm understanding of mechanical vibrations and differential equations. The book presents a historical context to the field of mechanical shock including numerous practical examples and anecdotes. Mathematical derivations of the fundamental principles and data processing methods are included and elucidated. Development of the single degree-of-freedom oscillatory theory and the theory of the shock response spectra are covered in detail in Chaps. 3 and 4. There vii viii Preface is a section on nonspectral techniques for analyzing shock test data. Various types of shock test machines and their capabilities are covered in Chap. 9. In addition, a lengthy discussion on the methods for deriving shock test specifications is included in Chap. 11. The analysis of multi-degree-of-freedom systems with shock response spectra is discussed in Chap. 8. The energy spectrum, which is another type of response spectrum that is used primarily in the earthquake engineering community, is discussed at the end of the book, in Chap. 12. Throughout the book, example problems illustrate the main concepts. Problems are included at the end of the chapters to further the reader’s understanding. Both authors have worked in the field of shock and vibration analysis and testing for many years. Our experience has been predominately with naval, aerospace, and spacecraft systems, although there has also been some brief work with earthquake survivability. Throughout our careers, we have found that a considerable amount of information about mechanical shock is available if one is willing to search. Unfortunately, the information is widely dispersed, and not every source is necessarily a good source. The finer points of the science are often buried in “black box” routines and analysis codes. A combined, handy reference, grounded in structural dynamic theory with wide applicability, has not been readily available. It is into this arena that the authors place this work. It is our hope that the reader will find the text useful and interesting. After all, mechanical shock is a fun business. Albuquerque, NM, USA Carl Sisemore Albuquerque, NM, USA Vít Babuška May 2019 Contents 1 Introduction ................................................................. 1 1.1 Introduction to Mechanical Shock ................................. 2 1.2 History of Shock Engineering ...................................... 4 1.2.1 Naval Shock ............................................... 5 1.2.2 Civil Engineering Shock .................................. 8 1.2.3 Aircraft Shock ............................................. 10 1.2.4 Space Vehicle Shock ...................................... 10 1.3 Effects of Shock on Systems ....................................... 13 1.3.1 Structural Failure .......................................... 13 1.3.2 Functional Failure ......................................... 14 1.4 The Need for Dynamic Analysis ................................... 15 1.5 Summary ............................................................ 18 Problems ..................................................................... 18 References.................................................................... 19 2 Common Mechanical Shock Environments ............................. 21 2.1 Impact Shock........................................................ 21 2.1.1 Transportation Shock ..................................... 24 2.1.2 Rail Shock ................................................. 27 2.2 Drop Shock.......................................................... 28 2.3 Pyroshock ........................................................... 31 2.3.1 Explosive Bolt Theory of Operation ..................... 34 2.4 Ballistic Shock ...................................................... 34 2.4.1 Recoil Theory ............................................. 36 2.4.2 Shot-to-Shot Dispersion .................................. 37 2.5 Seismic Shock....................................................... 38 2.6 Underwater Shock .................................................. 40 2.7 Summary ............................................................ 43 Problems ..................................................................... 43 References.................................................................... 44 ix x Contents 3 Single Degree-of-Freedom Systems ....................................... 45 3.1 SDOF Governing Equations........................................ 46 3.2 Solution of the Differential Equation .............................. 52 3.3 Free Vibration ....................................................... 52 3.3.1 Free Vibration of Undamped SDOF Systems............ 53 3.3.2 Free Vibration of Damped SDOF Systems .............. 53 3.4 Forced Response .................................................... 58 3.4.1 Basic Shock Excitation ................................... 58 3.4.2 General Shock Excitation ................................. 68 3.5 Summary ............................................................ 82 Problems ..................................................................... 83 References.................................................................... 84 4 Shock Environment Characterization Using Shock Response Spectra ....................................................................... 87 4.1 History of the Shock Response Spectra............................ 89 4.1.1 Shock Spectra