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On similitude law of sub-systems

Zach Liang1 and George C. Lee2

  1. Department of Civil Structural and Environmental Engineering, University at Buffalo, State University of New York,
    Buffalo, New York, USA

  2. Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo, State University of New York,
    Buffalo, New York, USA

Abstract: Based on Buckingham's π-Theorem, dimensional analysis has achieved considerable success over the past near-century. Model testing has long been a powerful tool in both scientific studies and engineering applications. However, the prototype objects are becoming more and more complicated nowadays, and many of the prototype systems can contain several sub-systems. The conventional theories on model-prototype similarity and dimensional analysis have only limited application since the π -Theorem itself does not distinguish between the original system and subsystems. This is particularly true in the field of structural dynamics, where the structure is often modeled as a multi-degree-of-freedom system. In this paper, we attempt to show that, if a system can be decoupled into several nontrivial subsystems, then, in each subsystem, the number of π -terms will be reduced and therefore simplify the model testing. On the other hand, if a system cannot be decoupled into subsystems, then using model testing with reduced π -term analysis, both experimentally and theoretically, may introduce severe errors.

Keywords: similitude law; Buckingham's π-theorem; model testing; sub-systems

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Copyright 2009 IEM. Journal of Earthquake Engineering and Engineering Vibration. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as described below, without written permission from the Publisher. Copying of articles is not permitted except for personal and internal use, to the extent permitted by national copyright law, or under the terms of a license issued by the National Reproduction Rights Organization of China.