Adaptive framework for FGPS bio-resonators with hollow microcore for mass detection combining nonlocal DQM computation

This study examines the adsorption-driven resonance shift in biomolecule–microresonator system, taking into account shear distortion, distributed adatoms, and small-scale effects. A dynamic behavior model for a functionally graded porous (FGP) resonator combining with a hollow microbeam is developed, integrating surface stress effects. The functional sandwich microbeam approach and localized biomolecule approach are applied, incorporating van der Waals (vdW) interactions via the Lennard–Jones (6–12) and Morse interatomic potentials to assess the impact of all applied conditions. The adsorption-induced energy is modeled using a distributional approach for both the bio-receptor and spike protein. The dynamic vibration equations are adapted to formulate the Euler–Bernoulli beam model (EBM) and the Levinson beam model (LBM), these models are subsequently solved using the Navier solution method (NSM) and the differential quadrature method (DQM) to evaluate the resonance frequency shift. Numerical findings indicate that the computed shift response is affected by perforation attributes, the presence of adsorbed adatoms, the intensity of the magnetic field, and the small-scale effects. In addition, the frequency shift depends on the active surface parameters, the adsorbed adatoms, and the localized receptor and spike, with interatomic phenomena contributing to the sandwich microsystem’s increased flexibility, that underscores the importance of including such phenomena in computations. Consequently, the proposed model is well-suited for studying the dynamic behavior of biomolecule-resonator systems and determining the mass and density of spikes and viruses in the presence of adatom bonds. The nonlocal dynamic behavior of adatom-microstructure systems is analyzed, providing insights crucial for advancing mass sensing technologies integrated into bio-microelectromechanical systems (Bio-MEMS).