Abstract This study investigates the nonlinear dynamic behavior and thermal stability of porous functionally graded material (FGM) nanobeams, with particular emphasis on the role of 1:3 internal resonance. In nano-electromechanical systems (NEMS), thermal environments may significantly reduce structural stiffness and limit the validity of purely linear predictions. To address this problem, the Nonlocal Strain Gradient Theory (NSGT) combined with von Kármán geometric nonlinearity is employed to establish a size-dependent nonlinear model. The governing equations are solved using the Method of Multiple Scales (MMS), and the analytical results are independently verified through fourth-order Runge–Kutta (RK4) numerical integration, showing excellent agreement with a relative error below 1%. The results indicate that, near the thermal buckling threshold, nonlinear coupling between the first and third vibration modes enables partial modal energy redistribution and supports stable post-buckling oscillations. In addition, geometric hardening behavior and the associated nonlinear backbone curves demonstrate the potential of the proposed system for thermally robust and frequency-tunable nanoresonator applications. The present study provides a unified theoretical framework for understanding the coupled effects of porosity, material gradation, thermal loading, and size dependency on the nonlinear response of advanced nanobeams.
Mustafa Oğuz Nalbant (Tue,) studied this question.