An Analytical Study on Thermally Induced Vibration Analysis of FG Beams Using Different HSDTs

Thermo-mechanical vibrations of functionally graded (FG) beams are developed. Governing equations of functionally graded beams are obtained based on higher-order variation of transverse shear strain through the depth of the beam. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion and boundary condition are derived from Hamilton’s principle. Beam is assumed under uniform thermal loading and simply supported boundary condition. Analytical solution is presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Numerical computations are performed for a functionally graded simply supported beam with a gradient index obeying power law and the results are displayed graphically and tabular to show the effects of the gradient index, temperature rise, and geometrical parameters on the fundamental natural frequency of FG beams, indicating that natural frequency is sensitive to the gradient variation of material properties, geometrical parameters, shear deformations and temperature rise.