Volume 24, Number 1, January–March 2018
|Page(s)||63 - 87|
|Published online||20 October 2017|
On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate
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.
Received: 24 March 2016
Accepted: 9 December 2016
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.
Mathematics Subject Classification: 35J40 / 35P15 / 74K20
Key words: Shape variation / eigenvalues / plates / torsional instability / suspension bridges
© EDP Sciences, SMAI 2017
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