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Hilbert spectrum and intrinsic oscillation mode of dynamic response of a bilinear SDOF system: influence of harmonic excitation amplitude

Zhang Yushan (张郁山)1, Liang Jianwen (梁建文)1 and Hu Yuxian (胡聿贤)2

  1. Department of Civil Engineering, Tianjin University, Tianjin 300072, China
  2. Institute of Geophysics, China Earthquake Administration, Beijing 100081, China

Abstract: Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.

Keywords: bilinear SDOF system; Hilbert-Huang transform (HHT); Hilbert spectrum; Hilbert marginal spectrum; Fourier spectrum; intrinsic mode function (IMF); intra-wave modulation; inter-wave combination

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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.