  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.
