Non-deformable Solid Mechanics Set
coordinated by Abdelkhalak El Hami
Volume 5
First published 2019 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
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 licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd
27–37 St George’s Road
London SW19 4EU UK
www.iste.co.uk
John Wiley & Sons, Inc.
111 River Street
Hoboken, NJ 07030
USA
www.wiley.com
© ISTE Ltd 2019
The rights of Georges Vénizélos and Abdelkhalak El Hami to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2019946982
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-036-2
This book is the fifth and last volume in the Non-deformable Solid Mechanics series. As with the first four volumes, its content is inspired by the mechanics teachings offered at the Conservatoire National des Arts et Métiers (CNAM) in France.
The authors, Georges Venizelos in Paris and Abdelkhalak El Hami in Rouen, took part in CNAM engineering training in their continuing education or apprenticeship training. They wish to pay tribute to their colleague, Michel Borel, equally passionate in teaching mechanics, who participated in creating the first four volumes but who passed away, alas, too early, before the creation of this fifth volume.
This book, Movement Equations 5, focuses on the dynamics of sets of non-deformable solids, thus completing this series. In this volume, appropriate mathematical tools (torsor calculus and matrix calculation) are used to obtain the movement equations of a chain of solids and solve them in order to obtain the information necessary for the design of mechanical systems.
Chapter 1 presents the direct application of the fundamental principle of dynamics to the movement of a chain of solids, as developed in the previous volumes of this series, assuming that each solid is considered non-deformable. Yet, when these solids are presented in the form of loops or branches, these are generally subject to structural strains like tensile, compression, bending or torsion during movement.
Having applied the fundamental principle of dynamics to the movement of a chain of solids, and obtained the movement equations of a linear system of solids, in Chapter 2 we study the vibration behavior of a system of n mass-spring-dampers. By passing to the limit, we describe the study of the vibrations of a continuous (deformable) system.
Chapter 3 presents the study of the vibrations of a rigid solid, those of a set of several solids and those of a deformable solid. It is based on knowledge of variations with respect to time, or frequency, of several parameters. The variations in these parameters with respect to time tend to be coupled. The movement equations of the mechanical set considered then constitute a second-order differential equation system.
The vibratory behavior of a deformable structure or of a set of solids connected by elastic links depends on the mechanical characteristics of the system and the amplitude and frequency of excitation.
In Chapter 4, we look to obtain the response of an excited system with respect to the excitation frequency.
Georges VÉNIZÉLOS
Abdelkhalak EL HAMI
August 2019
and 
and 
passing through point O
towards 
and 
and 
or 
or 
in the frame 〈λ〉
, independent of point P
When the situation of the solid (S) in the frame 〈λ〉 is represented by the parameters Qα, we state : 
where
