On Computational Solution of the Dynamic and Static Behaviour of a Coupled Thermoelastic Timoshenko Beam

The Timoshenko beam theory caters for transverse shear deformations, which are more pronounced in short beams. Previous works were examined, and Hamilton’s principle was used in deriving the governing equation. This research considers two dimensions (2-D): heat and displacement response. A more comprehensive mathematical expression that incorporates this 2-D model on the vibration of a coupled Timoshenko thermoelastic beam and axial deformation effect is formulated. The significance of this model will be expressed through its finite element method (FEM) formulation. The results compared favourably with those of previous works. It was re-established that the amplitude of deflections, as well as cross-sectional rotations, increases considerably as the aspect ratio of the beam decreases. In this way, for larger aspect ratios, the response of the beam is like the quasi-static heating condition. This is expected since the increase in the aspect ratio of the beam reduces its structural stiffness and consequently its natural frequencies. So, the amplitude and temporal period of its vibrations become greater. The beam under the applied thermal loading experiences thermally-induced vibrations. Also, the dynamic solution is substantially influenced by the coupling between strain and temperature fields. The results also reveal that the aspect ratio of the beam could have a significant impact on the vibratory response of the beam. Specifically, it is proportional to the amplitude and temporal period of the thermally-induced vibrations of the beam.