Predicting Dynamic Response of Nonlocal FGP Bio-Resonator with Coupled Surface Effects Merging vdW Interaction–Based Interatomic Potentials

This study investigates adsorption–induced resonance shifts in biomolecule-microresonator systems, accounting for shear distortion, distributed adatoms, and small–scale influences. A dynamic model is formulated for a functionally graded porous (FGP) resonator with a hollow microbeam, integrating surface stress effects. The aim of this study is to develop a comprehensive model for the dynamic behavior of biomolecule–microresonator systems by incorporating multiple coupled effects, including van der Waals (vdW) interactions, magnetic fields, porosity, and perforation. The originality of the work lies in the integration of nonlocal elasticity theory with both Lennard–Jones and Morse potentials within a hollow functionally graded porous sandwich microbeam model, which has not been simultaneously addressed in previous studies. The analysis applies a functional sandwich microbeam framework and a localized biomolecule approach, incorporating van der Waals (vdW) interactions via Lennard–Jones (6–12) and Morse potentials to evaluate all influencing parameters. Adsorption–induced energy is represented through a distributional approach for both bio-receptors and spike proteins. The vibration equations are constructed using the Euler–Bernoulli beam model (EBM) and Levinson beam model (LBM), with solutions derived through the Navier solution method (NSM) and the differential quadrature method (DQM) to determine resonance frequency shifts. Numerical analysis reveals that the frequency shift response is dictated by perforation characteristics, adsorbed adatoms, magnetic field strength, and small–scale effects. Furthermore, the shift is influenced by active surface parameters, receptor-spike interactions, and adatom adsorption, with interatomic forces enhancing the flexibility of the sandwich microsystem. These findings emphasize the necessity of incorporating such interactions in computational models. The proposed approach effectively examines biomolecule–resonator dynamics and determines the mass and density of spikes and viruses in the presence of adatom bonds. Additionally, the study assesses the nonlocal dynamic behavior of adatom–microstructure systems, offering critical insights for refining mass sensing technologies in bio-microelectromechanical systems (Bio–MEMS).