Mathematical Models of Reissner-Mindlin Thermoviscoelastic Plates
We here investigate mathematical models describing deformations and thermal variations of a thin homogeneous thermoviscoelastic plate. First, a hereditary non-Fourier constitutive law for the heat flux and some heat power constitutive equation with linear memory are considered. Then, we adapt to hereditary relations some approximation procedures previously established for thermoelastic plates and due to Lagnese and Lions [5, 6]. The resulting models are derived in the framework of the well-established theory of heat conduction, thanks to Gurtin and Pipkin, and according to the standard approximation procedure for the Reissner-Mindlin plate model.
We consider a homogeneous, (thermally and elastically) isotropic plate of the Mindlin type, subject to thermal deformations and hereditary heat conduction law. We assume that the plate is of uniform thickness \(d\)
- 2.Giorgi C, Naso MG (2006) Mathematical models of Reissner-Mindlin thermoviscoelastic plates. J Thermal Stress 29(7):699–716Google Scholar
- 4.Gurtin ME (1971/1972) Time-reversal and symmetry in the thermodynamics of materials with mem-ory. Arch Rational Mech Anal 44:387–399Google Scholar
- 5.Lagnese J, Lions JL (1988) Modelling analysis and control of thin plates, Recherches en Mathématiques Appliquées [Research in Applied Mathematics], vol 6. Masson, ParisGoogle Scholar
- 9.Naso MG (2000) Exponential stability of a viscoelastic plate with thermal memory. Riv Mat Univ Parma 6(3):37–56Google Scholar
- 14.Chandiramani N, Librescu L (1989) Dynamic stability of transversely isotropic viscoelastic plates. J Sound Vib 130(3):467–486Google Scholar