On the interrelation of divergence, flutter and auto-parametric resonance

Herrmann, G.; Hauger, Werner

doi:10.1007/bf00533072

Cited by 13 publications

(10 citation statements)

References 7 publications

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“…Take θ in the form (28) and plug it into (30) ; then multiply (30) by sin ( π L x ) and integrate over (0, L ). Several terms cancel due to (31) : if an odd number of skew-symmetric functions is involved then the integral over (0, L ) vanishes.…”

Section: Lemmamentioning

confidence: 99%

“…A recent mathematics text [51] , for example, seeking an application for a developed theory of parametric resonance, attempts to explain the Tacoma Narrows failure through this phenomenon . We refer to [15,28,31] for connections between (aerodynamic) parametric resonance, flutter theory, and self-oscillations, also applied to suspension bridges.…”

Section: Introductionmentioning

confidence: 99%

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Torsional instability in suspension bridges: The Tacoma Narrows Bridge case

Arioli

Gazzola

2017

Communications in Nonlinear Science and Numerical Simulation

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All attempts of aeroelastic explanations for the torsional instability of suspension bridges have been somehow criticised and none of them is unanimously accepted by the scientific community. We suggest a new nonlinear model for a suspension bridge and we perform numerical experiments with the parameters corresponding to the collapsed Tacoma Nar- rows Bridge. We show that the thresholds of instability are in line with those observed the day of the collapse. Our analysis enables us to give a new explanation for the torsional instability, only based on the nonlinear behavior of the structure

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Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Torsional instability in suspension bridges: The Tacoma Narrows Bridge case

Arioli

Gazzola

2017

Communications in Nonlinear Science and Numerical Simulation

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“…All these phenomena seem to be somehow related. For instance, parametric resonance is shown to be connected with flutter, see [66,140], while Jenkins [152, p. 178] writes first that In self-oscillating "aeroelastic flutter", including the motion of the bridge . .…”

Section: Partial Explanations Of Thementioning

confidence: 99%

Mathematical Models for Suspension Bridges

Gazzola

2015

MS&A

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“…In fact, the thresholds for flutter and for internal resonance are linked by the well-known formula for the kinetic energy (18) E c = k V 2 c , for some k > 0 depending on the air density. We refer to [21,37,40] for a clear explanation of the relationship between flutter and internal resonance.…”

Section: Thresholds For the Torsional Stabilitymentioning

confidence: 99%

On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate

2017

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Abstract. We consider a partially hinged rectangular plate and its normal modes. There are two families of modes, longitudinal and torsional. We study the variation of the corresponding eigenvalues under domain deformations. We investigate the possibility of finding a shape functional able to quantify the torsional instability of the plate, namely how prone is the plate to transform longitudinal oscillations into torsional ones. This functional should obey several rules coming from both theoretical and practical evidences. We show that a simple functional obeying all the required rules does not exist and that the functionals available in literature are not reliable.

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On the interrelation of divergence, flutter and auto-parametric resonance

Cited by 13 publications

References 7 publications

Torsional instability in suspension bridges: The Tacoma Narrows Bridge case

Torsional instability in suspension bridges: The Tacoma Narrows Bridge case

Mathematical Models for Suspension Bridges

On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate

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