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International audienceIn 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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“…shows that the constrained system described by (8) is divergence unstable by an additional kinematic con-…”

Section: Results In a Finite Dimension And Position Of The Problemmentioning

confidence: 99%

On the stability of nonconservative continuous systems under kinematic constraints

Lerbet

Challamel

Nicot³

et al. 2017

Z. Angew. Math. Mech.

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Continuous Divergence KISS

Lerbet¹,

Challamel²,

Nicot³

et al. 2020

Stability of Discrete Non-Conservative Systems

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Large deflections of inextensible cantilevers: modeling, theory, and simulation

Deliyianni

Gudibanda

Howell

et al. 2020

Math. Model. Nat. Phenom.

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A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam’s inextensibility —local arc length preservation—rather than traditional extensible effects attributed to fully restricted boundary conditions. Enforcing inextensibility leads to: nonlinear stiff- ness terms, which appear as quasilinear and semilinear effects, as well as nonlinear inertia effects, appearing as nonlocal terms that make the beam implicit in the acceleration. In this paper we discuss the derivation of the equations of motion via Hamilton’s principle with a Lagrange multiplier to enforce the effective inextensibility constraint . We then provide the functional framework for weak and strong solutions before presenting novel results on the existence and uniqueness of strong solutions. A distinguishing feature is that the two types of nonlinear terms prevent independent challenges: the quasilinear nature of the stiffness forces higher topologies for solutions, while the nonlocal inertia requires the consideration of Kelvin-Voigt type damping to close estimates. Finally, a modal approach is used to produce mathematically-oriented numerical simulations that provide insight to the features and limitations of the inextensible model.

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Cited by 5 publications

References 16 publications

On the stability of nonconservative continuous systems under kinematic constraints

On the stability of nonconservative continuous systems under kinematic constraints

Continuous Divergence KISS

Large deflections of inextensible cantilevers: modeling, theory, and simulation

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