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Implementation of configuration dependent stiffness proportional damping for the dynamics of rigid multi-block systems

Yun Byeong Chae1 and Jae Kwan Kim2

  1. R & D Division, Chungsuk Engineering, 57, Garak-dong, Songpa-ku, Seoul, 138-802, Korea
  2. School of Civil, Urban and Geosystem Engineering, Seoul National University, Seoul, 151-742, Korea

Abstract: The distinct element method (DEM) has been used successfully for the dynamic analysis of rigid block systems. One of many difficulties associated with DEM is modeling of damping. In this paper, new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid multi-block systems. The stiffness proportional damping is constructed for the prescribed damping ratio, based on the non-zero fundamental frequency effective during the time interval while the boundary conditions remain essentially constant. At this time interval, the fundamental frequency can be estimated without complete eigenvalue analysis. The damping coefficients will vary while the damping ratio remains the same throughout the entire analysis. A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases. These procedures were implemented in the development of the distinct element method for the dynamic analyses of piled multi-block systems. The analysis results for the single-block and two-block systems were in a good agreement with the analytic predictions. Applications to the seismic analyses of piled four-block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.

Keywords: multi-block systems; stiffness proportional damping; rocking; impact; distinct element method; rigid body dynamics

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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.