Thermo-elastic buckling and free vibration behavior of functionally graded beams with various materials gradation laws

An analytical method is presented for thermo-elastic buckling and free vibration behavior of radially graded beams made of functionally graded (FG) materials with different material gradation laws using linear, power and exponential functions. The temperature-dependent material properties of the FG beams are obtained as functions of radial position and different material gradation laws using linear, power and exponential functions. Thermal fields of the radially graded FG beams are obtained using one dimensional Fourier law of heat conduction equation for different material gradation laws. Next, using kinematics and constitutive relationship, thermo-elastic stress and strain, resultant normal force, transverse shear forces and bending moment are obtained and using Hamilton’s principle equations of motion are obtained for buckling and free vibration behavior of the FG beams. On the basis of analytical formulation, a computer code in MATLAB is developed and validated with the existing results of material properties, buckling loads and natural frequencies. Finally, a parametric study is carried out to understand the importance of material, temperature, and geometric parameters on thermo-elastic buckling and vibration behavior of the FG beams. Numerical results show that the material and temperature parameters have comparatively high impact for the prediction of the thermo-elastic behavior of the FG beams.

Figure: Thick-walled functionally graded cylinder: a coordinate and b cross-sectional geometry and variation of c \({\Delta T}_{cr}^{NLTD}\) ${\mathrm{\Delta }T}_{\mathit{cr}}^{\mathit{NLTD}}$ for \(k=3\) $k=3$ and (d) \({\Delta T}_{cr}^{ETD}\) ${\mathrm{\Delta }T}_{\mathit{cr}}^{\mathit{ETD}}$ , with different \(L/\left({R}_{o}-{R}_{i}\right)\) $L/\left(R_o,-,R_i\right)$ and end conditions for the (SUS304/Si₃N₄) beam.

Thermo-elastic buckling and free vibration behavior of radially functionally graded circular hollow beams under thermal loads are studied. Temperature field and material properties are evaluated for the graded beams using material gradation laws. Critical buckling temperature and free vibration of the beams are derived, importance of material grading, temperature, geometric parameter are examined.