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A method for stochastic seismic response analysis of non-classically damped structures

Xu Qing(徐清)1, Gao Cunchen (高存臣)1 and Wang Junjie(王君杰)2

  1. China Ocean University, Qingdao 266003, China

  2. National Key Laboratory for Disaster Reduction of Civil Engineering, Tongji University, Shanghai 200092, China

Abstract: A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression . The method is developed in the frequency domain. The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response). Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy. This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy.

Keywords: non-classically damped structures; random response; modal correlation coefficients

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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.