Geodesic
On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate
Berchio, Elvise1  ; Buoso, Davide1 ; Gazzola, Filippo2 
1 Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
2 Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 63-87

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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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016076
Classification : 35J40, 35P15, 74K20
Keywords: Shape variation, eigenvalues, plates, torsional instability, suspension bridges

Berchio, Elvise 1 ; Buoso, Davide 1 ; Gazzola, Filippo 2

1 Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
2 Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy. 
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     title = {On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {63--87},
     publisher = {EDP-Sciences},
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Berchio, Elvise; Buoso, Davide; Gazzola, Filippo. On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 63-87. doi: 10.1051/cocv/2016076

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