Nonlocal FG porous adsorber with 2D PSH network under magnetic intensity for large frequency range considering vdW interaction potentials

Abstract In this contribution, the nonlocal frequency shift is investigated and analyzed for an adatoms-microstructure system, considering the effects of nonlocal behavior, adatom distribution, and magnetic field. The microstructure is a sandwich microbeam including face sheets that are functionally graded porous (FGP) and a longitudinally perforated core with a uniform periodic square hole’s network (PSH) arranged parallel to the length of the sandwich microbeam. The material characteristics for three layers are assumed to change along the thickness correspondingly to a power law function, where Maxwell’s equations are exploited to express how the applied magnetic field has been affected. Eringen’s nonlocal elasticity is utilized to incorporate small-scale behavior. At the same time, van der Waals interactions between the adatom itself and the adatom microstructure substrate are established employing Lennard-Jones (6–12) and Morse potentials to account for the energy induced by adsorption. The dynamic equations of vibration are modified to develop the Euler–Bernoulli beam model (EBM) and Levinson beam model (LBM), which are then solved using Navier solution method (NSM) and differential quadrature method (DQM) to determine the resonance shift. Numerical results revealed that the calculated shift response was influenced by the perforation characteristics, adsorbed adatoms, magnetic field intensity, and small-scale behavior. Consequently, numerical results are discussed to investigate the nonlocal dynamic response of adatom-microstructure systems, which are relevant to developing mass sensing devices incorporated into micro/nanoelectromechanical systems (M/NEMS).