Vibration analysis of functionally graded nanobeam in thermal environment

Abstract

Functionally graded (FG) nanobeams, as a key application of functionally graded materials (FGMs), demonstrate unique thermomechanical properties that make them particularly suitable for Micro-electromechanical Systems (MEMS) and other nanoscale applications. This study presents an analytical approach for investigating their vibration characteristics under linear and nonlinear temperature fields. The model integrates Euler–Bernoulli beam theory with nonlocal elasticity theory, thereby simultaneously capturing material gradation effects and size-dependent phenomena. A novel analytical framework is developed by applying the transfer function method (TFM) for the first time to the nonlocal Euler–Bernoulli beam model, enabling efficient analytical solution for natural frequencies. Unlike traditional numerical methods, the proposed method enhances computational efficiency and allows unified treatment of various boundary conditions. Numerical studies are conducted to comprehensively evaluate the effects of environment fields, constituent volume distribution, slenderness ratio, nonlocal parameters, and boundary conditions on the vibration behavior of FG nanobeams. The results offer valuable insights for the design and optimization of MEMS devices, thermally stressed aerospace components, and microscale biomedical structures operating in complex thermal environments.