Thermal effect on the dynamic behavior of nanobeam resonator assuming size-dependent higher-order strain gradient theory

The temperature change and size scale dependent effects on the dynamical behaviors of the Carbon nanotube (CNT)-based nano-resonator are investigated in this work. The equation of motion of the CNT-based nano-resonator incorporating the higher-order strain gradient deformation, the geometric nonlinearity due to von Karman nonlinear strain, and the thermal effects is derived. A Galerkin based modal decomposition is used to investigate both the free vibration and forced vibration of the nano-resonator. The temperature variation effect is analyzed by assuming both low and high temperature environments. The results show that when assuming a high temperature in the post buckling regime, the nano-resonator natural frequencies dispersion graph shows possibilities of modes-veering and modes-crossing variation due to the initial buckling of the nano-resonator. From the forced-vibration analysis, the results demonstrate that taking into consideration the higher-order strain gradient deformation in modeling the CNT based nano-resonator completely changes the frequency response of the CNT-based nanoresonator.