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Structural Engineering and Mechanics
  Volume 76, Number 4, November25 2020 , pages 451-463
DOI: https://doi.org/10.12989/sem.2020.76.4.451
 


A semi-analytical study on the nonlinear pull-in instability of FGM nanoactuators
Mohamed A. Attia and Rasha M. Abo-Bakr

 
Abstract
    In this paper, a new semi-analytical solution for estimating the pull-in parameters of electrically actuated functionally graded (FG) nanobeams is proposed. All the bulk and surface material properties of the FG nanoactuator vary continuously in thickness direction according to power law distribution. Here, the modified couple stress theory (MCST) and Gurtin-Murdoch surface elasticity theory (SET) are jointly employed to capture the size effects of the nanoscale beam in the context of Euler-Bernoulli beam theory. According to the MCST and SET and accounting for the mid-plane stretching, axial residual stress, electrostatic actuation, fringing field, and dispersion (Casimir or/and van der Waals) forces, the nonlinear nonclassical equation of motion and boundary conditions are obtained derived using Hamilton principle. The proposed semi-analytical solution is derived by employing Galerkin method in conjunction with the Particle Swarm Optimization (PSO) method. The proposed solution approach is validated with the available literature. The freestanding behavior of nanoactuators is also investigated. A parametric study is conducted to illustrate the effects of different material and geometrical parameters on the pull-in response of cantilever and doubly-clamped FG nanoactuators. This model and proposed solution are helpful especially in mechanical design of micro/nanoactuators made of FGMs.
 
Key Words
    semi-analytical solution; pull-in instability; freestanding behavior; FG nanobeams; integrated couple stress-surface energy model
 
Address
Mohamed A. Attia: Mechanical Design and Production Dept., Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt
Rasha M. Abo-Bakr: Deptartment of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
 

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