Modeling of Thermoviscoelasticity Time Harmonic Variational Problem for a Thin Wall Body

The paper presents the construction and analysis of vibration problem of thermoviscoelastic shells under the influence of non-stationary heat and under forced loads. The studied model was based on application of simplest finite element semidiscretization to mixed variational problem of dynamical thermoviscoelasticity. The problem in addition to the mutual influence of temperature field and stress field is also taken into account the viscoelastic properties of the material thin wall body. For assumptions quite suitable for applications we prove the well-posedness forthis model of time harmonic vibrations.