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Studies in Applied Mechanics 50

R ot a t i ng S h e l l Dy n a m i c s

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Studies in Applied Mechanics 50

Rotating Shell Dynamics

Hua LiComputational MEMS Division,Institute ofHigh Performance

Computing, Singapore

K.Y. LamDepartment ofMechanical Engineering,

National University of

Singapore, Singapore

T.Y. NgSchool ofMechanical and Production Engineering,

Nanyang Technological

University, Singapore

2005

Amsterdam Boston Heidelberg London New York Oxford

Paris San Diego San Francisco Singapore Sydney Tokyo
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First edition 2005

Library of Congress Cataloging in Publication Data

Li, Hua.

Rotating shell dynamics/Hua Li, K.Y. Lam, T.Y. Ng. 1sted. p. cm. (Studies in applied mechanics ; 50)

Includes bibliographical references and index.

ISBN 0-08-044477-6 (alk. paper)

1. Shells (Engineering) I. Lam, Khin Yong. II. Ng, T. Y. (Teng Yong) III. Title. IV.

Series.

TA660.S5L453 2004624.17762 dc22

A catalog record is available from the Library of Congress.

British Library Cataloguing in Publication Data

A catalogue record is available from the British Library.

2004057705

ISBN: 0-08-044477-6

1 The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper).Printed in The United Kingdom.
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Dedicated to Duer, Anne and my parents for their constant encouragement

Hua Li

To Karen, Derrick and Rachel for their support and encouragement

K.Y. Lam

Dedicated first and foremost to GOD, and to my wife, Lay Keow

T.Y. Ng

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vii

PREFACE

There are numerous engineering applications for high-speed rotating shell structures which rotate about their symmetric axes,

and this is especially so in aerospace industries. Although there are many published books on shell dynamics, almost all of

them do not involve the dynamics of rotating shells. Physically, the important distinctions between rotating and non-rotating

shells of revolution are the presence of Coriolis and centrifugal accelerations as well as the hoop tension arising in rotating

shells due to the angular velocities. These effects have significant influences on the dynamic behaviors of the rotating shells. For

example, the frequency characteristics of a shell structure are generally determined by the shell geometry, material properties,

boundary conditions and externally applied loads. However, when the shell rotates, the structural frequency

characteristics are qualitatively altered. This qualitative difference manifests itself in the form of a bifurcation

phenomenon in the natural frequency parameters. For a stationary shell of revolution, the vibration of the shell is a standing

wave motion. However, when the same shell rotates, the standing wave motion is transformed, and depending on the

direction of rotation, backward or forward travelling waves will emerge.

Due to the distinct differences from generic stationary shells, and their wide-ranging engineering applications, a

comprehensive study is therefore warrantedfor the full understanding of rotating shell dynamics. In the latter half of the last

decade, such a study was performed by the authors. Much of this research was carried out in the context of graduate

research work, with Professor Khin-Yong Lam (current co-author) of the National University of Singapore supervising a

group of graduate students in this focus area. The two other current co-authors were then PhD research scholars in this very

vibrant group. The idea of collating and systematically documenting this research was first hatched in June 2002 when the

authors were attending a scientific meeting in Philadelphia. Amazingly, we acted upon it upon our return to Singapore! The

present monograph is written with a view to share the key developments and integral findings of the above research with the

research community. In this monograph, a complete theoretical platform detailing of the fundamental theory for rotating

shells of revolution is established. Dynamic problems such as free vibration and dynamic stability are examined in detail,

for basic shells of revolution such as cylindrical and conical shells. The influences of various parameters on the

dynamic behaviors, including rotating speed, boundary condition, initial pressure, geometrical and material properties, wave

number, etc., are investigated in various parametric studies.

This work represents the first monographic text fully dedicated to the dynamic behaviors of rotating shell structures. It

aims to provide both the casual and interested reader with insights into the special features and intricacies of shell dynamics

when rotation is involved, and covers the basic derivation of the dynamic governing equations for rotating shells.

Benchmark results for free vibration, critical speed, and parametric resonance are also documented. It is written in as simple

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