Doublet structural modeling of nonhomogeneous Euler mass sensor nanobeams using boundary characteristics Bernstein Polynomials

Abstract This study investigates the doublet structural model for analyzing nonhomogeneous Euler mass sensor nanobeams, incorporating the concept of doublet mechanics alongside Bernstein polynomials (BPs). BPs serve as basic functions within the Rayleigh–Ritz method, facilitating conversional governing equations into a geikneralized Eigenvalue problem. The study further employs orthogonal Bernstein polynomials (OBPs) for enhanced computational precision. By incorporating a mass sensor mechanism, the model leverages nanobeam sensitivity to detect small mass variations for nanoscale applications. Additionally, the research examines variable material properties and a range of boundary conditions, with significant emphasis on the effects of nondimensional frequency, normal stress, displacement, scaling effect parameter, beam length, doublet mechanics parameter, nonlocal parameter, and resonant frequency. A comparative analysis is carried out to validate the existing results and a good agreement is arrived. This study's results may be useful for the optimal and safety design of nano‐electro‐mechanics systems.