Adsorption‐induced frequency analysis using nonlocal Euler‐Bernoulli beam theory with initial axial stress

Abstract

Purpose

The purpose of this paper is to study the buckling and the vibration of the beam induced by atom/molecule adsorption using the nonlocal Euler‐Bernoulli beam model with initial axial stress.

Design/methodology/approach

The nonlocal parameter associated with adsorbed mass and bending rigidity variations of the beam induced by adsorbates are taken into account, and the buckling and dynamic behaviors are obtained via the Hamilton's principle, in which the potential energy between adsorbates and surfaces of the beam, the bending energy, the external work and the kinetic energy are summed as the Lagrangian function.

Findings

The results show that, for both buckling and resonant frequency, the nonlocal effect should be considered when the beam scales down to several hundreds of nanometres, especially for higher mode numbers.

Originality/value

The present paper gives the exact expressions for the buckling and resonant frequency of a simple‐supported nonlocal beam with initial axial stress. Different from previous works, the mass increasing and bending rigidity of the beam are found size‐dependent (nonlocal effect), resulting in possible different static and dynamic behaviors of the beam when atom/molecular adsorption occurs. The exact expressions obtained for the buckling and resonant frequency may be helpful to the design and application of micro‐ and nanobeam‐based sensors/resonators.

Citation

Xu, X. and Deng, Z. (2013), "Adsorption‐induced frequency analysis using nonlocal Euler‐Bernoulli beam theory with initial axial stress", Multidiscipline Modeling in Materials and Structures, Vol. 9 No. 1, pp. 116-127. https://doi.org/10.1108/15736101311329197