Size-dependent investigation of the 2D-FG CNTRC nanobeams using nonlocal strain gradient beam theory subjected to hygro-thermo conditions

Abstract

In the present study, the vibration frequency and wave propagation investigation of the multidirectionally FG nanobeams reinforced with carbon nanotubes is studied comprehensively for the first time. A nonlocal model including both softening and stiffness enhancement impacts of the nanosize beam according to nonlocal strain gradient beam theory is presented to consider the size-dependent effect. The transverse response is separated into bending and shear parts to consider the shear impacts exactly. The effects of the moisture and thermal fields are considered nonlinearly through the thickness according to the comprehensive relations. Hamilton’s principle is utilized to achieve the dynamic equations of motion, whereas an analytical solution method is utilized to find the vibration characteristics of the nanobeam for several boundary conditions. The simulation results indicate that by reducing/raising the FG indexes, the impacts of the strain gradient coefficient on the frequency of the nanobeam will increase/decrease.