Functional resonator-based nonlocal FGP hollow adsorber for wide detection of coupled biomolecules using DQM framework

This study examines the resonance frequency shift due to adsorption in a biomolecule-resonator sandwich nanobeam system under a temperature-induced load. The analysis incorporates shear deformation, distributed adatoms, and small-scale effects within the framework of nonlocal elasticity theory (NET). The sandwich nanobeam consists of three sections: a perforated core with a uniform square-hole pattern and two bonded functionally graded porous (FGP) layers. Adsorption-induced energy is modeled using a distribution-based approach for spike proteins and bio-receptors. The dynamic model of the nanobeam resonator integrates surface stress effects. The functional nanobeam and localized biomolecule models are used in conjunction with van der Waals (vdW) forces, employing the Lennard–Jones (6–12) and Morse potentials to assess all influencing factors. Shear force and inertia moment are explicitly derived from the nonlocal Timoshenko beam equations, with residual stress considered as an additional axial load. The Navier technique and differential quadrature method (DQM) are employed to solve the motion equations, enabling a comprehensive interpretation of the results. Numerical findings reveal that surface properties, adsorbed adatoms, perforation dimensions, hole number, thermal loads, variation in power law index, porosity parameters, and the positioning of receptors and spikes all influence the frequency shift. Results further indicate that interatomic interactions reduce system stiffness, emphasizing their significance in computational analysis. The proposed model effectively evaluates the dynamic response of biomolecule-resonators and can determine the mass and density of viruses and spikes while accounting for adatom bonding effects.