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R. Heuer:
"Nonlinear thermomechanical vibrations of bimodular beams";
Talk: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2019), Vienna, Austria; 2019-02-18 - 2019-02-22.

The present paper is concerned with the modelization and numerical solution of the transient response of Bernoulli-Euler beams due to thermal excitation. The beam is assumed to be homogeneous and simply supported. However, it is composed of a bimodular material, thus behaving differently in tension and compression.
Assuming a time-variant (nonlinear) temperature distribution across the beam´s cross-section its influence is considered by defining cross-sectional means of thermal strain and thermal curvature.
When deriving the equations of motion for flexural oscillations an advanced procedure is developed by defining an effective composite layered structure with discontinuous natural beam axis depending on the sign of deflection´s amplitude. The position of the natural axis follows from a nonlinear equation that is dependent on both the geometry of the cross-section and the elastic material properties.
By means of a semi-analytical method, using a modified Galerkin-procedure to discretize spatially and the Newmark beta method for time wise discretization, parameter studies are performed for the load cases "imposed time-harmonic thermal curvature" and "thermal shock".
The results are compared to those derived with alternative integration schemes.