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Size-dependent nonlinear vibration of an electrostatic nanobeam actuator considering surface effects and inter-molecular interactions

  • Saman Esfahani
  • Siamak Esmaeilzade KhademEmail author
  • Ali Ebrahimi Mamaghani
Article

Abstract

In this paper, the size-dependent nonlinear vibration of an electrostatic nanobeam actuator is investigated based on the nonlocal strain gradient theory, incorporating surface effects. A comprehensive model regarding the von Karman geometrical nonlinearity, inter-molecular forces and both components of the electrostatic excitation (AC and DC) is proposed to explore the system behavior near the primary resonance. Utilizing Hamilton’s principle, the nonlinear equation of motion of the system is derived. The natural frequency and dynamic response of the system, comprising frequency and force response diagrams, are obtained analytically via multiple scales technique in conjunction with the differential quadrature method and validated through a numerical approach. The roles of the nonlocal and strain gradient parameters, surface elasticity, inter-molecular forces and quality factor on the system oscillations are examined. The acquired results unveiled that the size-dependent parameters can significantly displace the multi-valued portions and instability thresholds of the dynamical response. Furthermore, it is deduced that the surface effects induce the stiffness hardening of the nanobeam, whereas the inter-molecular forces impose the stiffness softening effect.

Keywords

Nanobeam actuator Nonlocal strain gradient theory Surface effects Inter-molecular forces Nonlinear vibration Differential quadrature method (DQM) 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTarbiat Modares UniversityTehranIran

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