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.

Accepted:

DOI: 10.1051/cocv/2016076

Keywords: Shape variation, eigenvalues, plates, torsional instability, suspension bridges

^{1}; Buoso, Davide

^{1}; Gazzola, Filippo

^{2}

@article{COCV_2018__24_1_63_0, author = {Berchio, Elvise and Buoso, Davide and Gazzola, Filippo}, 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}, volume = {24}, number = {1}, year = {2018}, doi = {10.1051/cocv/2016076}, mrnumber = {3764134}, zbl = {1400.35092}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016076/} }

TY - JOUR AU - Berchio, Elvise AU - Buoso, Davide AU - Gazzola, Filippo TI - On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 63 EP - 87 VL - 24 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016076/ DO - 10.1051/cocv/2016076 LA - en ID - COCV_2018__24_1_63_0 ER -

%0 Journal Article %A Berchio, Elvise %A Buoso, Davide %A Gazzola, Filippo %T On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 63-87 %V 24 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016076/ %R 10.1051/cocv/2016076 %G en %F COCV_2018__24_1_63_0

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, Volume 24 (2018) no. 1, pp. 63-87. doi : 10.1051/cocv/2016076. http://archive.numdam.org/articles/10.1051/cocv/2016076/

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