Izuru Takewaki - An Impulse and Earthquake Energy Balance Approach in Nonlinear Structural Dynamics

First edition published 2021
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2021 Izuru Takewaki and Kotaro Kojima

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Library of Congress Cataloging-in-Publication Data
Names: Takewaki, Izuru, author. | Kojima, Kotaro, author.
Title: An impulse and earthquake energy balance approach in nonlinear structural dynamics / Izuru Takewaki, Kotaro Kojima.
Description: First edition. | Boca Raton, FL : CRC Press, 2021. | Includes bibliographical references and index.
Identifiers: LCCN 2021000740 (print) | LCCN 2021000741 (ebook) | ISBN 9780367681401 (hardcover) | ISBN 9780367681418 (paperback) | ISBN 9781003134435 (ebook)
Subjects: LCSH: Earthquake engineering. | Force and energy.
Classification: LCC TA654.6 .T3424 2021 (print) | LCC TA654.6 (ebook) | DDC 624.1/762--dc23
LC record available at https://lccn.loc.gov/2021000740
LC ebook record available at https://lccn.loc.gov/2021000741

ISBN: 978-0-367-68140-1 (hbk)
ISBN: 978-0-367-68141-8 (pbk)
ISBN: 978-1-003-13443-5 (ebk)

Typeset in Sabon
by SPi Global, India

On April 14 and 16, 2016, two consecutive large earthquakes occurred in Kumamoto, Japan. In most countries, it is a common understanding that building structures are designed to resist once to the ground motion from a large earthquake, e.g., one with the intensity level 7 (the highest level on the Japan Meteorological Agency scale; approximately XXII on the Mercalli scale), during its service life. However, in case of the Kumamoto earthquakes, a number of buildings were subjected to such large ground motions twice in a few days. This phenomenon was unpredictable, and the authors were convinced during and immediately after the earthquake that the critical excitation method is absolutely necessary for enhancing the earthquake resilience of building structures and engineering systems.

The senior author believed for a long time that near-fault ground motions have peculiar characteristics with a few simple waves (see ). The response to impulses can be described by the continuation of free vibration components, and this fact leads to the straightforward derivation of responses of even elastic-plastic structures.

Figure 0.1 Simple modeling of Rinaldi Station fault-normal component (Northridge EQ. 1994) as representative of near-fault ground motion: (a) one-cycle sinusoidal wave modeling, (b) 1.5-cycle sinusoidal wave modeling.

Figure 0.2 Impulse modeling of near-fault ground motion: (a) one-cycle sinusoidal wave and double impulse, (b) 1.5-cycle sinusoidal wave and triple impulse (Kojima and Takewaki 2015a).

In this monograph, the critical excitation problems for elastic-plastic structures under double and triple impulses are explained with the interval of impulses as a variable parameter (Kojima and Takewaki 2015a, b). Furthermore, the critical excitation problems for elastic-plastic structures under multiple impulses as a representative of long-period and long-duration ground motions are tackled with the interval of impulses as a variable parameter (Kojima and Takewaki 2015c, Kojima and Takewaki 2017). This approach can overcome the difficulty, called the nonlinear resonance, encountered first around 1960 in the field of nonlinear vibration, and the critical excitation problems for elastic-plastic structures are tackled in a more direct way than the conventional methods including laborious computation (see ). It can be said that the approach explained newly in this monograph opened the door for an innovative field of nonlinear dynamics.

Table 0.1 Conventional method and proposed method.

In principle, the method explained in this monograph is based on the energy balance law, which is taught as part of a high school physics course. Therefore, undergraduate students can read and understand this work. The authors hope that this monograph is also useful for graduate students for research and structural designers/engineers for practice.

Izuru Takewaki

Kotaro Kojima

Kyoto, 2020

1. K. Kojima and I. Takewaki ( 2015 a). Critical earthquake response of elastic-plastic structures under near-fault ground motions (Part 1: Fling-step input) , Frontiers in Built Environment (Specialty Section: Earthquake Engineering), Volume , Article 12.
2. K. Kojima and I. Takewaki ( 2015 b). Critical earthquake response of elastic-plastic structures under near-fault ground motions (Part 2: Forward-directivity input) , Frontiers in Built Environment (Specialty Section: Earthquake Engineering), Volume , Article 13.
3. K. Kojima and I. Takewaki ( 2015 c). Critical input and response of elastic-plastic structures under long-duration earthquake ground motions , Frontiers in Built Environment (Specialty Section: Earthquake Engineering), Volume , Article 15.