Publication

Abstract : The vibrational behavior of bi-directional functionally graded non-uniform Timoshenko nanobeam under linear and nonlinear temperature profiles has been investigated using first order shear deformation theory together with Eringen's nonlocal elasticity theory. The mechanical properties of beam material are assumed to be temperature dependent and temperature variation is applied across the thickness. The material composition varies according to a power-law distribution in thickness direction and as an exponential function in axial direction. Non-uniformity of beam's cross-section is along thickness and width both. The governing differential equations for such a beam model have been obtained using Hamilton's energy principle and numerically solved for different combinations of clamped, simply supported and free boundary conditions, namely, clamped-clamped, clamped-simply supported, simply supported-simply supported and clamped-free employing generalized differential quadrature method. The effect of temperature profiles, cross-sectional non-uniformity, functionally gradient indices along the thickness and length, slenderness ratio together with nonlocal parameter have been studied on the vibration characteristics of nanobeam for the first three modes of vibration and all the boundary conditions. Results have been validated with published work.