Size-Dependent Higher Order Thermo-Mechanical Vibration Analysis of Two Directional Functionally Graded Material Nano beam

This paper represented a numerical technique for discovering the vibrational behavior of a two-directional FGM (2-FGM) Nano beam exposed to thermal load for the first time. Mechanical attributes of two-directional FGM (2-FGM) Nano beam are changed along the thickness and length directions of nanobeam. The nonlocal Eringen parameter is taken into the nonlocal elasticity theory (NET). Uniform temperature rise (UTR), linear temperature rise (LTR), non-linear temperature rise (NLTR) and sinusoidal temperature rise (STR) during the thickness and length directions of Nano beam is analyzed. Third-order shear deformation theory (TSDT) is used to derive the governing equations of motion and associated boundary conditions of the two-directional FGM (2-FGM) Nano beam via Hamilton’s principle. The differential quadrature method (DQM) is employed to achieve the natural frequency of two-directional FGM (2-FGM) Nano beam. A parametric study is led to assess the efficacy of coefficients of two-directional FGM (2-FGM), Nonlocal parameter, FG power index, temperature changes, thermal rises loading and temperature rises on the non-dimensional natural frequencies of two-directional FGM (2-FGM) Nano beam.