Adaptive coupling of Buckingham–Coulomb potential for double porous microresonator with smart hollow core for biomolecule nanomass detection

This study develops a novel multiphysics framework to analyze the size-dependent dynamic response of a bioresonator microsystem designed for biomolecular nanomass detection. The proposed structure consists of a double microbeam sandwich configuration with functionally graded porous (FGP) layers and a perforated hollow microcore, whose thickness-dependent properties follow a power-law distribution with an uneven porosity pattern. Unlike previous studies limited to local elasticity or simplified adsorption models, this work introduces, for the first time, an adaptive coupling between the Buckingham–Coulomb potential and a double porous hollow bioresonator governed by nonlocal strain gradient theory (NSGT) under compressive loading. This unified formulation simultaneously captures short-range intermolecular forces, long-range electrostatic interactions, and competing nonlocal-strain gradient size effects within a single sensing platform. In the other hand, the dynamic behavior is modeled using both the Euler-Bernoulli (EBM) and Rayleigh (RBM) beam theories within a coupled vibration framework, enabling assessment of rotary inertia contributions at micro-scales. Van der Waals (vdW) interactions between distributed Ebola virus (EBOV) particles and bioresonator atoms are represented using both Morse and Buckingham–Coulomb potentials to evaluate adsorption-induced energy variations. The governing equations are solved via the Navier-type solution (NTM) and the differential quadrature method (DQM) for validation. The results reveal that the dimensionless frequency shift is highly sensitive to perforation geometry, porosity distribution, adsorption density, and compressive load, producing non-monotonic sensitivity trends not observed in single-beam or classical-local models. Furthermore, the interplay between coupling spring stiffness, small-scale parameters, and hollow-core flexibility induces a pronounced stiffness-softening effect, significantly enhancing mass-detection sensitivity. These findings provide new physical insight into the design optimization of high-performance porous microresonator biosensors.