Dynamic pull-in stability of torsional nano/micromirrors with size-dependency, squeeze film damping and van der Waals effect

Recently, electrostatic torsional nanomirrors are applied widely in various industries. In previous lectures, coefficient of squeeze film air damping in the gap between main plate and substrate has been constant, while this coefficient is the function of viscosity and air pressure and has nonlinear equation. In this paper, the effect of nonzero initial conditions also, and the effect of nonlinear coefficient of squeeze film air damping on the stability of torsional nanomirrors using higher order continuum theories are investigated. First considering two-degree-of-freedom coupled bending/torsion system, the governing equations of system are derived, then using the fourth order Runge-Kutta method and nonzero initial conditions, the equations of motion are solved. Dynamic pull-in instability voltage is obtained and by plotting of response curves and phase portraits, the size effect is investigated. Study of phase portraits shows that size effect causes increasing in the range of stability of nanomirror and increasing of length scale parameter increases the mentioned surface area. As well as assuming constant squeeze film air damping causes the error in investigating of its behavior. Therefore in equation of motion, for getting more accurate response, this coefficient must be considered nonlinear.