Thermal vibrations of temperature-dependent functionally graded non-uniform Timoshenko nanobeam using nonlocal elasticity theory

Vibration analysis for functionally graded non-uniform Timoshenko nanobeam under linear and nonlinear temperature profiles across the thickness has been presented on the basis of first order shear deformation theory together with Eringen's nonlocal elasticity theory. The material properties are taken to be temperature dependent and graded in thickness direction according to a power-law distribution. Non-uniformity of the cross-section is arising due to linear variations in thickness and width through the length of the beam. Numerical results have been obtained employing generalized differential quadrature method for solution procedure of the present model. The effect of nonuniformity in cross-section, slenderness ratio, gradient index, nonlocal parameter and temperature profiles on the vibration characteristics and mode shapes have been discussed. The efficacy of present results has been verified by comparing the results with published work.