On the stability problem of Nicolai with variable cross-section and compressibility effect

Seyranian, Alexander P.; Glavardanov, V.B.

doi:10.1016/j.ijsolstr.2013.09.014

Cited by 2 publications

(4 citation statements)

References 11 publications

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“… 2014 ; Luongo et al. 2014 ; Seyranian and Glavardanov 2014 ), see Fig. 1 c, thus entailing instability; the presence of a small asymmetry, that we label with a parameter , is able to shift the critical load of a small amount only (Seyranian and Mailybaev 2011 ; Seyranian et al.…”

Section: The Nicolai Paradoxmentioning

confidence: 97%

“…( 2014 ), Luongo et al. ( 2014 ) and Seyranian and Glavardanov ( 2014 ), for the Nicolai paradox, and in D’Annibale et al. ( 2015 ) for the Failure of the ‘similarity principle’.…”

Section: Appendix: Asymptotic Analysismentioning

confidence: 99%

“…( 2014 ), Luongo et al. ( 2014 ) and Seyranian and Glavardanov ( 2014 ), the splitting mechanism of the semi-simple eigenvalue (here ), is described by the formula (see “ Appendix ” for details): where are the first sensitivities of the coalescent eigenvalues. Accordingly, the trivial equilibrium is asymptotically stable when , i.e.…”

Section: The Nicolai Paradoxmentioning

confidence: 99%

“…( 2014 ), Luongo et al. ( 2014 ) and Seyranian and Glavardanov ( 2014 ). An extension of the problem to second-order perturbations was also performed in Luongo and Ferretti ( 2014 ).…”

Section: Introductionmentioning

confidence: 97%

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Paradoxes in dynamic stability of mechanical systems: investigating the causes and detecting the nonlinear behaviors

Luongo¹,

Ferretti²,

D’Annibale³

2016

SpringerPlus

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A critical review of three paradoxical phenomena, occurring in the dynamic stability of finite-dimensional autonomous mechanical systems, is carried out. In particular, the well-known destabilization paradoxes of Ziegler, due to damping, and Nicolai, due to follower torque, and the less well known failure of the so-called ‘principle of similarity’, as a control strategy in piezo-electro-mechanical systems, are discussed. Some examples concerning the uncontrolled and controlled Ziegler column and the Nicolai beam are discussed, both in linear and nonlinear regimes. The paper aims to discuss in depth the reasons of paradoxes in the linear behavior, sometimes by looking at these problems in a new perspective with respect to the existing literature. Moreover, it represents a first attempt to investigate also the post-critical regime.

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Section: The Nicolai Paradoxmentioning

confidence: 97%

“…( 2014 ), Luongo et al. ( 2014 ) and Seyranian and Glavardanov ( 2014 ), for the Nicolai paradox, and in D’Annibale et al. ( 2015 ) for the Failure of the ‘similarity principle’.…”

Section: Appendix: Asymptotic Analysismentioning

confidence: 99%

Section: The Nicolai Paradoxmentioning

confidence: 99%

“…( 2014 ), Luongo et al. ( 2014 ) and Seyranian and Glavardanov ( 2014 ). An extension of the problem to second-order perturbations was also performed in Luongo and Ferretti ( 2014 ).…”

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations