Nonlinearities in thermo-mechanical response of lightweight adsorber with fG-X CNT-reinforced composite core resting on elastic foundation under vdW interactions

This study aims to develop a comprehensive nonlinear dynamic model for a microstructure system with adsorbed atoms, accounting for the combined effects of nonlocal interactions, adatom distribution patterns, nonlinear elastic foundation, and thermal loading. The microstructure is modeled as a sandwich microbeam composed of two perforated face sheets containing a longitudinal array of periodic square holes (PSH) and a microcore made of functionally graded carbon nanotube-reinforced composite (FG-CNTRC), resting on a nonlinear foundation. Two carbon nanotube patterns are examined, namely the uniform distribution (UD) and functionally graded (FG-X) configurations. Geometric nonlinearity is incorporated using the von Kármán nonlinear strain assumption, while the size-dependent response is described through nonlocal strain gradient. Adsorption-induced interactions are included by employing Lennard-Jones (6–12) and Morse potentials to represent vdW forces. The nonlinear governing equations are derived based on the Euler-Bernoulli and Levinson beam theories. The Galerkin method reduces system to an equation with cubic nonlinearity, and resonance shift is obtained using the method of multiple scales (MMS). Numerical results for the O/Si (100) system show that perforation properties, CNT distribution, thermal loading, elastic foundation, and small-scale effects significantly influence the response. These findings demonstrate the strong potential of such microstructures for M/NEMS-based mass sensing applications.