Scale Dependent Dynamic Behavior of Nano-wire Based Sensor in Accelerating Field


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The accelerating fields (e. g. centrifugal acceleration, constant acceleration) can change physical performance of nano-sensors significantly. Herein, a new size-dependent model is developed to investigate the dynamic and pull-in instability behavior of nanowire-fabricated sensor operated in an accelerating field. The scale dependent equation of motion is developed by employing a combination of the strain gradient theory (SGT) and the Gurtin–Murdoch elasticity (GME). Furthermore, the impact of rare field gas damping, structural damping and dispersion forces are included in the developed model. A semi-analytical solution is presented for calculating the stability parameters. Effects of different phenomena including centrifugal force, microstructure dependency, surface layer, length-scale-parameter, dispersion forces, rare field gas and structural damping on the dynamic stability parameters are demonstrated.

Key Words: Nanowire, Centrifugal force, Strain gradient elasticity, Dynamic instability, Surface energies.

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With the novel manufacturing methods for producing ultra-small structures, the applications of nanowires have increased rapidly in the various branch of nanotechnology. A typical nanowire-fabricated sensor is manufactured from a moveable nanowire parallel to a solid plate. The NEMS sensors have wide applications in modern measurement systems. These structures can be employed in satellite{5*}, automotive sensors{5**}, centrifuge devices for separating the solids form liquids, fault detection of roller bearing, measurement of high-speed spindle errors in CNC, balancing power plant rotating equipment [8], and angular speed detection of turbo-machinery. In the above mentioned applications, the sensor operated in an accelerating field which can significantly alter the behviour of the sensors. Miniature structure usually have considerable surface-to-volume ratio, therefore, the surface layer might play significant role on the behaviour of these structures. Gurtin-Murdoch surface elasticity (GME) is an efficient theory for incorporating the surface layer in miniature structures modelling. This theory has been employed by previous researchers for simulating the impacts of surface layer on the instability characteristics. Rather than surface layer, microstructure dependency might change the mechanical performance of ultra-small structures. The conventional elasticity is not able to simulate the scale dependency. Therefore, the non-classical microstructure dependent theories have been presented to incorporate the microstructure dependency in the simulation.

When the nanosensor is mounted on the a rotating machine, the angular velocity of the shaft can change the dynamic behavior of the sensor, significantly. History and phase portraits of the nano-sensor for different values of angular velocities at the corresponding pull-in voltage. It should be noted that the results of figure 10 are related to a sensor mounted inside the rotary wile figure 11 shows the dynamic behavior of a sensor mounted outside the rotary.

On the other hand, it is also inferred that as the speed of the rotating shaft increases dynamic pull-in instability happens at higher values of dynamic pull-in deflection. In contrast, when the nano-sensor mounted outside the rotary the pull-in time of the nano-bridge is enhanced by increasing the angular velocity and the pull-in phenomenon occurred at higher values of applied DC voltage. On the other hand, it is also inferred that as the speed of the rotating shaft increases, dynamic pull-in instability happens at higher values of dynamic pull-in deflection.

In this work, the SGT is incorporated with GME to develop a newsize dependent model for analyzing the effect of centrifugal acceleration on the instability behavior of nanowire-fabricated nano-sensor. The influences of rare field gas damping, the surface energy, the scale dependency and the dispersion forces on the dynamic instability parameters of the nanowire-fabricated nano-sensor subjected to centrifugal acceleration is investigated. An analytical solution based on the RRM is presented for investigating the instability parameters. The obtained results revealed that:

  • When the nano-sensor mounted inside the rotary the pull-in voltage of nano-sensor reduced by increasing the angular velocity, however, when the nano-sensor mounted outside the rotary the pull-in voltage of nano-sensor incresed by increasing the angular velocity.
  • The impacts of the surface energies on the instability voltage of nanowire-fabricated nano-sensor depends on the martial surface characteristic. For positive values, the surface layer enhance the instability voltage. However, for negative values, the surface layer reduce the instability voltage.
  • At a critical values of dispersion forces and surface layer elastic parameters, the freestanding nano-sensor pulls-in to the fixed ground.
  • By increasing the size parameter, the instability voltage of the sensor enhances.
  • When the flow damping is incorporated in the simulations, the stable center node convert to a stable focus node.

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