Influence of Modal Coupling on the Nonlinear Dynamics of Augusti’s Model

Orlando, Diego; Gonçalves, Paulo B.; Rega, Giuseppe; Lenci, Stefano

doi:10.1115/1.4003880

Cited by 16 publications

(9 citation statements)

References 26 publications

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“…For both models, the overall threshold of the escape region is obtained as the envelope of the different loci of local bifurcations-obtained by extensive numerical simulations of Eq. ( 4)-which govern the onset of escape in various frequency ranges (Orlando et al, 2011). Note that the main resonance occurs for an X ¼ x e =x p value (e.g., X ¼ 1=3 for the perfect model) which corresponds to the fundamental parametric resonance x e ¼ x s of the considered s.d.o.f.…”

Section: A the Model Of Augustimentioning

confidence: 98%

“…Consistent with the general scope of this Focus Issue on "50 Years of Chaos," this paper aims at highlighting the meaningfulness of chaos control, in its extended notion, as regards the design of discrete and continuous systems liable to subcritical buckling, which is an important research area in structural mechanics and engineering; attention is focused on systems where the interaction of different stable buckling modes with equal or nearly equal critical loads leads to coupled unstable post-buckling paths. Among them, model of Augusti (1964) has been used in the stability literature for many decades as an archetypal model of such behaviour (Orlando et al, 2011). Another model exhibiting coincident buckling loads, studied previously by Thompson and Hunt (1984), is a simplified model of a guyed tower consisting of an inverted pendulum stiffened by three linear inclined springs.…”

Section: Introductionmentioning

confidence: 99%

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Controlling practical stability and safety of mechanical systems by exploiting chaos properties

Lenci

Orlando

Rega

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, a method for controlling the global nonlinear dynamics of mechanical systems is applied to two models: the model of Augusti and an inverted guyed pendulum. These simplified models represent a large class of structures liable to buckling exhibiting interacting buckling phenomena. These structures may fail at load levels well below the theoretical buckling load due to complex nonlinear phenomena that decrease the safety and the dynamic integrity of the structure; this often occur as a consequence of imperfections and of the erosion of the basins of attraction of the safe pre-buckling solutions. So, it is of paramount practical importance to increase the safety of these structures in a dynamic environment. This can be achieved by increasing the integrity of the basins of attraction of the safe solutions, a goal that is attained by a control method which consists of the (optimal) elimination of homoclinic (or heteroclinic) intersection by properly adding superharmonic terms to a given harmonic excitation. By means of the solution of an appropriate optimization problem, it is possible to select the amplitudes and the phases of the added superharmonics in such a way that the manifolds distance is as large as possible. The results show that this methodology increases the integrity of the basins of attraction of the system and, consequently, the practical safety of the structure.

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Section: A the Model Of Augustimentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Controlling practical stability and safety of mechanical systems by exploiting chaos properties

Lenci

Orlando

Rega

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Therefore, safe practical applications need to be related to uncorrupted basins. Under this assumption, several studies have been conducted under the name of dynamical integrity (Lenci and Rega, 2004, Rega and Lenci, 2005, Rega and Alaggio, 2009, Gonc¸alves et al, 2011, Orlando et al, 2011, and bifurcation control is an interesting alternative to avoid instability issues. De Paula et al (2012) employed the chaos control approach in order to perform bifurcation control in a parametrically excited pendulum.…”

Section: Introductionmentioning

confidence: 99%

Experimental bifurcation control of a parametric pendulum

Paula

Savi

Vaziri

et al. 2015

Journal of Vibration and Control

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The aim of the study is to maintain the desired period-1 rotation of the parametric pendulum over a wide range of the excitation parameters. Here the Time-Delayed Feedback control method is employed to suppress those bifurcations, which lead to loss of stability of the desired rotational motion. First, the nonlinear dynamic analysis is carried out numerically for the system without control. Specifically, bifurcation diagrams and basins of attractions are computed showing co-existence of oscillatory and rotary attractors. Then numerical bifurcation diagrams are experimentally validated for a typical set of the system parameters giving undesired bifurcations. Finally, the control has been implemented and investigated both numerically and experimentally showing a good qualitative agreement.

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“…In [24,25], a two-dimensional reduced-order model of a cylindrical shell is considered, and, apparently for the first time, basins of attraction of dimension larger than two have been used in a preliminary way to evaluate the dynamical integrity. The dynamical integrity of Augusti's model is preliminarily considered in [26], and then reconsidered in depth in [27] together with the dynamical integrity of a similar archetypal model of a guyed tower. For this type of systems, the load carrying capacity is the main mechanical performance, and thus in [28,29] the relationships between load carrying capacity and dynamical integrity have been investigated in depth.…”

Section: Introductionmentioning

confidence: 99%

“…The dynamical integrity of Augusti's model is preliminarily considered in [26], and then reconsidered in depth in [27] together with the dynamical integrity of a similar archetypal model of a guyed tower. For this type of systems, the load carrying capacity is the main mechanical performance, and thus in [28,29] the relationships between load carrying capacity and dynamical integrity have been investigated in depth.…”

Section: Introductionmentioning

confidence: 99%

The dynamical integrity concept for interpreting/ predicting experimental behaviour: from macro- to nano-mechanics

Lenci

Rega

Ruzziconi

2013

Phil. Trans. R. Soc. A.

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The dynamical integrity, a new concept proposed by J.M.T. Thompson, and developed by the authors, is used to interpret experimental results. After reviewing the main issues involved in this analysis, including the proposal of a new integrity measure able to capture in an easy way the safe part of basins, attention is dedicated to two experiments, a rotating pendulum and a micro-electro-mechanical system, where the theoretical predictions are not fulfilled. These mechanical systems, the former at the macro-scale and the latter at the micro-scale, permit a comparative analysis of different mechanical and dynamical behaviours. The fact that in both cases the dynamical integrity permits one to justify the difference between experimental and theoretical results, which is the main achievement of this paper, shows the effectiveness of this new approach and suggests its use in practical situations. The men of experiment are like the ant, they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes the middle course: it gathers its material from the flowers of the garden and field, but transforms and digests it by a power of its own. Not unlike this is the true business of philosophy (science); for it neither relies solely or chiefly on the powers of the mind, nor does it take the matter which it gathers from natural history and mechanical experiments and lay up in the memory whole, as it finds it, but lays it up in the understanding altered and digested. Therefore, from a closer and purer league between these two faculties, the experimental and the rational (such as has never been made), much may be hoped. (Francis Bacon 1561-1626) But are we sure of our observational facts? Scientific men are rather fond of saying pontifically that one ought to be quite sure of one's observational facts before embarking on theory. Fortunately those who give this advice do not practice what they preach. Observation and theory get on best when they are mixed together, both helping one another in the pursuit of truth. It is a good rule not to put overmuch confidence in a theory until it has been confirmed by observation. I hope I shall not shock the experimental physicists too much if I add that it is also a good rule not to put overmuch confidence in the observational results that are put forward until they have been confirmed by theory. (Arthur Stanley Eddington 1882-1944)

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Influence of Modal Coupling on the Nonlinear Dynamics of Augusti’s Model

Cited by 16 publications

References 26 publications

Controlling practical stability and safety of mechanical systems by exploiting chaos properties

Controlling practical stability and safety of mechanical systems by exploiting chaos properties

Experimental bifurcation control of a parametric pendulum

The dynamical integrity concept for interpreting/ predicting experimental behaviour: from macro- to nano-mechanics

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