Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam

Luongo, Angelo; D’Annibale, Francesco

doi:10.1177/1081286516632381

Cited by 27 publications

(8 citation statements)

References 37 publications

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“…The nonlinear nature of the analyzed mechanical system implies that many features that are difficult to be tackled (see, e.g., [65][66][67][68][69] in the context of nonlinear vibrations, [70,71] in the context of nonlinear motions as well as [72][73][74][75][76] in dynamic stability of mechanical systems). Therefore, having a formulation that is as simple as possible is always an opportunity to pursue.…”

Section: Conclusion: Present and Future Challengesmentioning

confidence: 99%

A discrete formulation of Kirchhoff rods in large-motion dynamics

Giorgio¹

2020

Mathematics and Mechanics of Solids

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A nonlinear model for the dynamics of a Kirchhoff rod in the three-dimensional space is developed in the framework of a discrete elastic theory. The formulation avoids the use of Euler angles for the orientation of the rod cross-sections to provide a computationally singularity-free parameterization of rotations along the motion trajectories. The material directions related to the principal axes of the cross-sections are specified using auxiliary points that must satisfy constraints enforced by the Lagrange multipliers method. A generalization of this approach is presented to take into account Poisson’s effect in an orthotropic rod. Numerical simulations are performed to test the presented formulation.

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Section: Conclusion: Present and Future Challengesmentioning

confidence: 99%

A discrete formulation of Kirchhoff rods in large-motion dynamics

Giorgio¹

2020

Mathematics and Mechanics of Solids

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“…However, this type of damping has a significant drawback, namely the low efficiency outside the region of resonance of the system. One way to solve this problem is to use a nonlinear viscous damper [4,5,8,11,12,[16][17][18]29] or a damper with hysteretic properties [9,28] (here we should note the recent work [13] where the effects of nonlinear hysteretic damping on the post-critical behavior of the viscoelastic Beck's beam are discussed). Particularly, in the well-known book [17] different forms of nonlinear damping (together with several examples) are presented and discussed completely especially from the point of view their effects on the nonlinear behavior of dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

“…Figure13. The relative motion of a car x(t) under single pulse affection for various kinds of damping.…”

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confidence: 99%

Efficiency of hysteretic damper in oscillating systems

Семенов

Solovyov

Meleshenko

et al. 2020

Math. Model. Nat. Phenom.

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This paper is dedicated to comparative analysis of nonlinear damping in the oscillating systems. More specifically, we present the particular results for linear and nonlinear viscous dampers, fractional damper, as well as for the hysteretic damper in linear and nonlinear (Duffing-like) oscillating systems. We consider a constructive mathematical model of the damper with hysteretic properties on the basis of the Ishlinskii-Prandtl model. Numerical results for the observable characteristics, such as the force transmission function and the ``force-displacement'' transmission function are obtained and analyzed for both cases of the periodic affection, as well as for the impulse affection (in the form of $\delta$-function). A comparison of an efficiency (in terms of the corresponding transmission functions) of the nonlinear viscous damper and the hysteretic damper is also presented and discussed.

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“…Recently a reassessment of the models needed to describe beam‐like structural elements has been used in order to simplify the tools needed to study nonlinear equilibrium shapes, loss of stability, buckling and post‐buckling phenomena like those studied in []. In particular in order to simplify the computation of the buckling load of a beam, its large deformations and its multiple stable equilibria discrete Hencky models have been recovered .…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of uniformly loaded Elastica: Experimental and numerical evidence of motion around curled stable equilibrium configurations

et al. 2019

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It has been numerically observed and mathematically proven that for a clamped Euler's Elastica, which is uniformly loaded, there exist, in large deformations, some ‘undocumented’ equilibrium configurations which resemble a curled pending wire. Even if Elastica is one of the most studied model in mathematical physics, we could not find in the literature any description of an equilibrium like the one whose existence was forecast theoretically in [36]. In this paper, we prove that this kind of equilibrium configurations can be actually observed experimentally when using ‘soft’ beams. We mean with soft beams: Elasticae whose ratio between the applied load intensity and the bending stiffness is large enough. Moreover, we prove experimentally that such equilibrium configurations are actually stable, by observing their oscillations around the considered nonstandard equilibrium configuration. To describe theoretically such oscillations we consider, instead of a ‘soft’ Elastica model, directly a Hencky‐type discrete model, i.e. a ‘masses‐springs’ finite dimensional Lagrangian model. In this way we formulate, avoiding the use of an intermediate continuum model, a model for which numerical simulations can be performed without the introduction of any further discretization. In this way, we can also predict quantitatively the motions of soft beams, in the regime of large displacements and deformations. Postponing to future investigations more careful quantitative measurements, we report here that it was possible to get a rather promising qualitative agreement between observed motions and predictive numerical simulations.

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Nonlinear hysteretic damping effects on the post-critical behaviour of the visco-elastic Beck’s beam

Cited by 27 publications

References 37 publications

A discrete formulation of Kirchhoff rods in large-motion dynamics

A discrete formulation of Kirchhoff rods in large-motion dynamics

Efficiency of hysteretic damper in oscillating systems

Nonlinear dynamics of uniformly loaded Elastica: Experimental and numerical evidence of motion around curled stable equilibrium configurations

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