Hollow core-based FGP bio-resonator incorporating coupled mass-driven wide response range via nonlocal parabolic shear strain framework

Abstract

This study aims to examine the adsorption-induced resonance frequency shift in a biomolecule-resonator system subjected to a magnetic field, considering shear distortion, distributed adatoms, and small-scale effects using nonlocal strain gradient elasticity theory (SGET). The theory includes two scale parameters that correspond to both strain gradient and nonlocal effects, enabling accurate modeling of size-dependent behaviors critical for biosensing applications. The goal is to develop a dynamic behavior model suitable for determining the mass and density of proteins and viruses. The microstructure is modeled as sandwich, with functionally graded porous (FGP) face sheets and hollow intercore, featuring two-dimensional periodic square holes (2D PSH) network. The material gradation properties across the graded layer are described according to a power-law function, while the porosity is represented using even and uneven distributions. The Levinson beam model (LBM) and the Euler–Bernoulli beam model (EBM) are developed by modifying the standard beam equations, and the governing equations are solved applying the Navier-type method (NTM) and the differential quadrature method (DQM) is implemented with the SBCGE technique for boundary conditions, which provides increased accuracy. The interaction-driven resonance is modeled through van der Waals (vdW) energy utilizing Morse and Lennard–Jones (6–12) potentials. The computations show that the computed nonlocal shift is influenced by the active surface, adsorbed adatoms, and localized receptor and proteins. Additionally, the response is affected by perforation properties, magnetic field, and small-scale effects, emphasizing the complex interaction between structural and environmental factors. The proposed model proves its effectiveness in analyzing the dynamic behavior, aiding in the precise determination of protein mass and density, and enhancing mass sensing technologies within micro/nanoelectromechanical systems M/NEMS.