E-Book Overview
This volume considers the shock response spectrum, its various definitions, its properties and the assumptions involved in its calculation. In developing the practical application of these concepts, the shock shapes most often used with test facilities are presented, together with their characteristics and indications of how to establish test configurations comparable with those of the real, measured environment. There follows a demonstration of how to meet these specifications using standard laboratory equipment - shock machines, electrodynamic exciters driven by a time signal or a response spectrum - with discussion of the limitations, advantages and disadvantages of each method.
E-Book Content
Mechanical Shock This page intentionally left blank Mechanical Vibration & Shock Mechanical Shock Volume II Christian Lalanne HPS HERMES PENTON SCIENCE First published in 1999 by Hermes Science Publications, Paris First published in English in 2002 by Hermes Penton Ltd Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licences issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: Hermes Penton Science 120 Pentonville Road London N1 9JN © Hermes Science Publications, 1999 © English language edition Hermes Penton Ltd, 2002 The right of Christian Lalanne to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. British Library Cataloguing in Publication Data A CIP record for this book is available from the British Library. ISBN 1 9039 9604 X Printed and bound in Great Britain by Biddies Ltd, Guildford and King's Lynn www.biddies,co.uk Contents Introduction List of symbols 1 Shock analysis 1.1. Definitions 1.1.1. Shock 1.1.2. Transient signal 1.1.3. Jerk 1.1.4. Bump 1.1.5. Simple (or perfect) shock 1.1.6. Half-sine shock 1.1.7. Terminal peak saw tooth shock (TPS) or final peak saw tooth shock (FPS) 1.1.8. Initial peak saw tooth shock (IPS) 1.1.9. Rectangular shock 1.1.10. Trapezoidal shock 1.1.11. Versed-sine (or haversine) shock 1.1.12. Decaying sinusoidal pulse 1.2. Analysis in the tune domain 1.3. Fourier transform 1.3.1. Definition 1.3.2. Reduced Fourier transform 1.3.3. Fourier transforms of simple shocks 1.3.3.1. Half-sine pulse 1.3.3.2. Versed-sine pulse 1.3.3.3. Terminal peak saw tooth pulse (TPS) 1.3.3.4. Initial peak saw tooth pulse (IPS) 1.3.3.5. Arbitrary triangular pulse 1.3.3.6. Rectangular pulse xi xiii 1 1 1 2 2 2 3 3 3 3 3 3 3 4 4 4 4 6 7 7 8 9 10 12 14 vi Mechanical shock 1.4 2 1.3.3.7. Trapezoidal pulse 1.3.4. Importance of the Fourier transform Practical calculations of the Fourier transform 1.4.1. General 1.4.2. Case: signal not yet digitized 1.4.3. Case: signal already digitized Shock response spectra domains 2.1. Main principles 2.2. Response of a linear one-degree-of-freedom system 2.2.1. Shock defined by a force 2.2.2. Shock defined by an acceleration 2.2.3. Generalization 2.2.4. Response of a one-degree-of-freedom system to simple shocks 2.3. Definitions 2.4. Standardized response spectra 2.5. Difference between shock response spectrum (SRS) and extreme response spectrum (ERS) 2.6. Algorithms for calculation of the shock response spectrum 2.7. Subroutine for the calculation of the shock response spectrum 2.8. Choice of the digitization frequency of the signal 2.9. Exampl