On the stability and instability criteria for circulatory systems: A review

Bulatović, Milica

doi:10.2298/tam201021013b

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…Interestingly, these structural models do not only display flutter instability but, similarly to the 'Ziegler's double pendulum', also counterintuitive behaviours, often referred as 'paradoxes' [37][38][39][40][41][42][43][44][45][46][47][48][49].…”

Section: (A) the Counterintuitive Character Of Flutter Instabilitymentioning

confidence: 99%

“…Recent theoretical works include studies of the integrability of the 'Ziegler's double pendulum' [50] and in general of mechanical systems with non-potential positional (circulatory) forces [51,52], destabilizing influence of circulatory forces on a degenerate equilibrium of a potential system [47][48][49], delay of flutter onset [53] and parametric instabilities in the 'Ziegler's double pendulum' with the periodic follower load [7], and stability of systems with follower forces under kinematic constraints [54].…”

Section: (A) the Counterintuitive Character Of Flutter Instabilitymentioning

confidence: 99%

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Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Bigoni,

Dal Corso,

Kirillov

et al. 2023

Proc. R. Soc. A.

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The phenomenon of oscillatory instability called ‘flutter’ was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps and new perspectives for investigations are indicated.

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Section: (A) the Counterintuitive Character Of Flutter Instabilitymentioning

confidence: 99%

Section: (A) the Counterintuitive Character Of Flutter Instabilitymentioning

confidence: 99%

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Bigoni,

Dal Corso,

Kirillov

et al. 2023

Proc. R. Soc. A.

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Stability of Multidegree of Freedom Potential Systems to General Infinitesimal Positional Perturbation Forces

Udwadia

Bulatović

2022

Journal of Applied Mechanics

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The stability of general linear multi-degree of freedom stable potential systems that are perturbed by general arbitrary positional forces, which may be neither conservative nor purely circulatory/conservative, is considered. It has been recently recognized that such perturbed potential systems with multiple frequencies of vibration are susceptible to instability, and this paper is centrally concerned with the situation when potential systems have such multiple natural frequencies. An approach based on perturbation theory that includes nonlinear terms in the expansions of the perturbed eigenvalues is developed. Explicit conditions under which the system either remains stable or becomes unstable due to flutter are provided. These results show that the stability/instability picture that emerges is far subtler and more complex than what might be intuitively inferred. The manner in which prior results related to narrower classes of perturbation matrices, like circulatory matrices, get included in the more general results obtained here is pointed out. Several numerical examples illustrate the applicability of the analytical results. An engineering application is provided demonstrating the power of the analytical results.

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On the stability and instability criteria for circulatory systems: A review

Cited by 2 publications

References 16 publications

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Stability of Multidegree of Freedom Potential Systems to General Infinitesimal Positional Perturbation Forces

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