Nonlinear Responses
Mechanics of rigid bodies in general is distinguished into Kinematics in which motions are described independently of their origin (e.g. the star-sprangled firmament), and Dynamics.
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The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series in to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECfURES- No. 342
NONLINEAR STABILITY OF STRUCTURES THEORY AND COMPUTATIONAL TECHNIQUES
EDITED BY A.N. KOUNADIS TECHNICAL UNIVERSITY OF ATHENS AND W.B. KRATZIG RUHR-UNIVERSITY BOCHUM
SPRINGER-VERLAG WIEN GMBH
Le spese di stampa di questo volume sono in parte coperte da contributi del Consiglio Nazionale delle Ricerche.
This volume contains 217 illustrations
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© 1995 by Springer-Verlag Wien Originally published by Springer-Verlag Wien New York in 1995
In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader.
ISBN 978-3-211-82651-5 DOI 10.1007/978-3-7091-4346-9
ISBN 978-3-7091-4346-9 (eBook)
PREFACE
The present volume, containing the full text of all papers presented at the course n-.). Eq.(16) shows that the integral curves (ellipses) are closed trajectories associated with periodic (but not,in general,harm~nic motion) of bounded amplitude around the stable equilibrium point (q ,A) which is a center. If the first nonzero term of even degree is negative [then V (q;q 0 ;}..) takes on a E T relative maximum reaching a position q0 ] the family of integral curves (15) behaves like [23] (v~o.
m=1,2, ... )
( 17)
The integral curves associated with eq. (17) are similar to branche! of hyperbolas with curvilinear asymptotes. The remote equilibrium point q D wpich the motion reaches (corresponding to maximum deflection, i.e. qD=q max ) is a saddle (unstable equilibrium) point. Via this point an escaped motion (dynamic buckling) occurs which may lead either to an "unbounded" motion or to a large displacement as shown in Fig. 2a and Fig. 2b ~ respectiv!ly. In the first case the motion is stable in the neighborhood of q (stability in the small) and unstable or "unbounded" in the large. In the second case the motion is unstable in the
81
Potential Systems
stable equilibrium points stable equilibrium point
q
saddle point
(a)
saddle point
(b)
Fig. 2. Typical phase-plane portraits showing an escaped undampe
