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On the numerical investigation of size and surface effects on nonlinear dynamics of a nanoresonator under electrostatic actuation

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Abstract

This study aims to investigate the influences of nanostructure parameter and surface elasticity parameters on the nonlinear vibration of a nanoelectromechanical system under double-sided electrostatic actuation. For this, the effects of size dependency and surface energy are modeled through applying the consistent couple-stress theory together with the Gurtin–Murdoch elasticity theory. Taking into account the midplane stretching effect for doubly clamped boundary conditions, the nonlinear strain–displacement relationship is considered based on the Euler–Bernoulli beam assumption. Hamilton’s principle is utilized in order to establish the governing differential motion’s equation, and reduced-order model is obtained through implementing Galerkin’s procedure. Bifurcation diagrams are plotted to capture the steady-state response of the system with varying the nondimensional parameter, the ratio of AC to DC voltage amplitude. The influences of the length-scale parameter, surface elasticity modulus and density, and residual surface stress on the system dynamic response have been explored. The results reveal that the pull-in excitation frequency is highly influenced by these parameters, and also the interval length of the bifurcation parameter corresponding to the periodic and chaotic motions is extremely shifted by the amount of couple-stress and residual surface stress parameters.

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Authors and Affiliations

  1. School of Mechanics Engineering, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran

    Sasan Rahmanian & Shahrokh Hosseini-Hashemi

  2. Mechanical Engineering Department, School of Engineering, Tarbiat Modares University, Tehran, Iran

    Mohammad-Reza Ghazavi

  3. Center of Excellence in Railway Transportation, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran

    Shahrokh Hosseini-Hashemi

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  1. Sasan Rahmanian
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  2. Mohammad-Reza Ghazavi
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  3. Shahrokh Hosseini-Hashemi
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Correspondence to Shahrokh Hosseini-Hashemi.

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Technical Editor: Wallace Moreira Bessa, D.Sc.

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Rahmanian, S., Ghazavi, MR. & Hosseini-Hashemi, S. On the numerical investigation of size and surface effects on nonlinear dynamics of a nanoresonator under electrostatic actuation. J Braz. Soc. Mech. Sci. Eng. 41, 16 (2019). https://doi.org/10.1007/s40430-018-1506-9

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  • DOI: https://doi.org/10.1007/s40430-018-1506-9

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