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The influence of dispersion forces on the dynamic pull-in behavior of vibrating nano-cantilever based NEMS including fringing field effect

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Sedighi H. M. , Daneshmand F. , Zare J.

Archives of Civil and Mechanical Engineering

2014

tom Vol. 14, no. 4

766--775

Dynamic pull-in instability of vibrating nano-actuators in the presence of actuation voltage is studied in this paper through introducing the closed form expression for the fundamental frequency of beam-type nano-structure. The fringing field effect and dispersion forces (Casimir and van der Waals attractions) are taken into account in the dynamic governing equation of motion. The influences of initial amplitude of vibration, applied voltage and intermolecular forces on the dynamic pull-in behavior and fundamental frequency are investigated by a modern asymptotic approach namely Parameter Expansion Method (PEM). It is demonstrated that two terms in series expansions are sufficient to produce an acceptable solution of the actuated nano-structure. The obtained results from numerical methods by considering three mode assumptions verify the strength of the analytical procedure. The qualitative analysis of system dynamic shows that the equilibrium points of the autonomous system include stable center points and unstable saddle nodes. The phase portraits of the nano-beam actuator exhibit periodic and homoclinic orbits.

Instability Characteristics of Free-Standing Nanowires Based on the Strain Gradient Theory with the Consideration of Casimir Attraction and Surface Effects

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Sedighi H. M. , Ouakad H. M. , Khooran M.

Metrology and Measurement Systems

2017

tom Vol. 24, nr 3

489--507

Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, the proximity force approximation (PFA) for small separations, and the Dirichlet asymptotic approximation for large separations with a cylinder-plate geometry are employed. A nonlinear governing equation of motion for free-standing nanowires – based on the Gurtin-Murdoch model – and a strain gradient elasticity theory are derived. To overcome the complexity of the nonlinear problem in hand, a Garlerkin-based projection procedure for construction of a reduced-order model is implemented as a way of discretization of the governing differential equation. The effects of length-scale parameter, surface energy and vacuum fluctuations on the dynamic instability threshold and adhesion of nanowires are examined. It is demonstrated that in the absence of any actuation, a nanowire might behave unstably, due to the Casimir induction force.

The effect of quintic nonlinearity on the investigation of transversely vibrating buckled Euler-Bernoulli beams

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Sedighi H. M. , Reza A. , Zare J.

2013

tom Vol. 51 nr 4

959--968

A new formulation of vibrations of the axially loaded Euler-Bernoulli beam with quintic nonlinearity is investigated in the present study. The beam nonlinear natural frequency as a function of the initial amplitude is obtained. In this direction, modern powerful analytical methods namely He’s Max-Min Approach (MMA) and Amplitude-Frequency Formulation (AFF) are employed to approximate the frequency-amplitude relationship of the beam vibrations. Afterwards, it is clearly shown that the first term in the series expansions is sufficient to produce a highly accurate approximation of the nonlinear system. Finally, preciseness of the present analytical procedures is evaluated in contrast with numerical calculation methods.