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On the stability of nonconservative continuous systems under kinematic constraints

Abstract : 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 in(Thorn)nite dimensional Hilbert spaces and non-self-adjoint operators.
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Jean Lerbet, Noël Challamel, François Nicot, Félix Darve. On the stability of nonconservative continuous systems under kinematic constraints. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Wiley-VCH Verlag, 2017, 97 (9), pp.1100--1119. ⟨10.1002/zamm.201600203⟩. ⟨hal-01518620⟩

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