Non-local response prediction for FGP sandwich microbeam with 2D PSH network subjected to adatoms-substrate interactions and exited by magnetic intensity

The present research contribution investigates a molecular resonant system’s adsorption-induced relative resonant frequency shift, considering the quality of distributed adatoms, the effect of shear distortion, and small-scale effects using non-local elasticity theory. We considered the structure’s several properties of perforation, sandwich, FGM, and porosity. The nanobeam structure can be considered a one-dimensional multi-property system. Using Eringen’s theory of elasticity, small-scale behaviour is modelled. To find the total energy transformation, the substrate-adatom energy and the adatom-adatom energy were calculated based on the van der Waals (vdW) interactions in the framework of the Morse potential and the Lennard–Jones (6–12) potential. The shear beam model (SBM) and the Euler beam model (EBM) were deduced by relying on the mechanical equations and modifying the coupled system equations. Computation was analysed analytically via the Navier-Type solution and numerically using the differential quadrature method. The SBM and EBM yield distinct relative frequency shifts, highlighting the importance of considering shear effects. The results indicate a significant dependency of the resonant frequency shift on the nanobeam’s structural properties and external conditions. This study provides a comprehensive understanding of the dynamic behaviour of multi-property nanobeams under various conditions. The findings can be applied to the design of advanced detection microdevices and microsensors.