Summary
The goal of this work is to extend the developed by the authors of this study a theoretical model of the vibration of bi-material beams subjected the combined action of mechanical and thermal loads. The geometrically nonlinear version of the Timoshenko beam theory is used to describe the theoretical model of the problem. Starting from the geometrical, constitutive and equilibrium governing equations of each layer of the bi-material beam are derived with respect to one coordinate system. In a contrast with the previously developed model, where a generalized properties of the beam were used, here the properties of each layer were taken into the equations of motion. Then reduced order models for the equations of each layer were developed using the normal forms of vibration. The relation between the generalized coordinates in time of the layers were obtained which was used in the solution of the equations of motion. Numerical results for the response of the beam in time and frequency domains were obtained and stability and bifurcation of the beam due to elevated temperature and loading parameters were studied.
