Shape sensitivity analysis for vibrating plate models

Wednesday 28 January 2015, h. 14:30, room 2BC30
Davide Buoso (Padova, Dip. Mat.)
"Shape sensitivity analysis for vibrating plate models"

In this talk, we consider two different models for the vibration of a clamped plate: the Kirchhoff-Love model, which leads to the well known biharmonc operator, and the Reissner-Mindlin model, which instead gives a system of differential equations. We point out similarities and differences, showing the connections between these two problems. Then we show some results concerning the stability of the spectrum with respect to domain perturbations.
After recalling the known results in shape optimization for the biharmomic operator, we state some analyticity results for the dependence of the eigenvalues upon domain perturbations and Hadamard-type formulas for shape derivatives. Using these formulas, we prove that balls are critical domains for the symmetric functions of the eigenvalues under volume constraint.