A Strain-Gradient Approach for Electromagnet Instability Analysis of Nano-Tweezers

The influence of an external magnetic field is a critical factor in determining the pull-in dynamics of ultra-small devices, particularly in the case of nano-tweezers. This study employs strain gradient elasticity to derive the size-dependent governing equation of nano-tweezers under the influence of an external longitudinal magnetic field. In addition to the magnetic field, we consider the effects of Coulomb attraction and Casimir forces, examining how finite dimensions impact both electrical and Casimir interactions. The nano-tweezers are modeled as two parallel cantilever Euler-Bernoulli beams with rectangular cross sections. By utilizing the Rayleigh-Ritz method to solve the constitutive equations, we explore various phenomena that affect the dynamic pull-in behavior of these nano-tweezers. Our findings reveal that applying a magnetic field substantially reduces the pull-in voltage of the nano-tweezers. The results of this paper provide valuable implications for the future development and optimization of nano-tweezers and similar ultra-small devices immersed in magnetic flux.

Keywords:

Magnetic field , Nano-tweezers , Casimir force , strain gradient theory