Vibration and thermal buckling analysis of rotating nonlocal functionally graded nanobeams in thermal environment

Abstract

A new nonlocal model for free vibration and thermal buckling analysis of rotating temperature-dependent functionally graded (FG) nanobeams in thermal environment is developed by introducing an axial nonlinear second-order coupling deformation based upon the Eringen's nonlocal elasticity theory (ENET) and Euler-Bernoulli beam theory (EBT). Material properties of FG nanobeams are assumed to be through-thickness symmetric and the temperature distribution is uniform in the thickness direction. The Hamilton's principle is utilized to derive the governing equations and associated boundary conditions of the nonlocal rotating FG nanobeam model considering thermal, small-scale and centrifugal stiffening effects. The nonlocal governing differential equations are transformed into algebraic eigenvalue equations evaluating the vibration and buckling properties through the Galerkin method. The validity and accuracy of the present nonlocal model are verified by convergence and comparative studies. Numerical results are presented to investigate the influences of dimensionless angular velocity, hub radius ratio, temperature change, material gradient index, slenderness ratio and nonlocal parameter on the natural frequencies and critical buckling temperatures of rotating FG nanobeams. The obtained results clearly show that these effects significantly affect the thermal buckling and vibrational behaviors of rotating FG nanobeams.