On the stability of nonconservative continuous systems under kinematic constraints

In this paper we deal with recent results on divergence kinematic structural stability (ki.s.s.) resulting from discrete nonconservative finite systems. We apply them to continuous nonconservative systems which are shown in the well‐known Beck column. When the column is constrained by an appropriate...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Mechanik 2017-09, Vol.97 (9), p.1100-1119
Main Authors: Lerbet, J., Challamel, N., Nicot, F., Darve, F.
Format: Article
Language:English
Subjects:
Columns (structural)
Divergence
Engineering Sciences
Hilbert basis
Hilbert spaces
kinematic constraint
Kinematic Structural Stability
Kinematics
Mechanics
non self‐adjoint operators
Structural stability
variational formulation
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Summary:In this paper we deal with recent results on divergence kinematic structural stability (ki.s.s.) resulting from discrete nonconservative finite systems. We apply them to continuous nonconservative systems which are shown in the well‐known Beck column. When the column is constrained by an appropriate additional kinematic constraint, a certain value of the follower force may destabilize the system by divergence. We calculate its minimal value, as well as the optimal constraint. The analysis is carried out in the general framework of inÞnite dimensional Hilbert spaces and non‐self‐adjoint operators. The authors deal with recent results on divergence kinematic structural stability (ki.s.s.) resulting from discrete nonconservative finite systems. They apply them to continuous nonconservative systems which are shown in the wellknown Beck column. When the column is constrained by an appropriate additional kinematic constraint, a certain value of the follower force may destabilize the system by divergence. They calculate its minimal value, as well as the optimal constraint. The analysis is carried out in the general framework of infinite dimensional Hilbert spaces and non‐self‐adjoint operators.
ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.201600203