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While experiments reveal that the mechanical response of nano-structures is size-dependent, classic continuum theories are not able to simulate this size effect. In this paper, a non-classic continuum theory e.g. modified couple stress theory is applied for modeling the size dependent instability of torsional nano-actuator. The constitutive equation of the actuator is derived taking the effect of electrostatic and molecular forces into account. Variation of the tilt angle as a function of the applied voltage is obtained and the instability parameters i.e. instability voltage and instability angle are determined. Two actuators with different cross-sectional torsional beams are investigated as case studies. Results show that when the thickness of the torsional beam is comparable with the intrinsic material length scale, size-dependency of material characteristics can highly affect the instability parameters of the actuator. The effect of van der Waals (vdW) molecular forces on the size-dependent instability is investigated. Furthermore, the minimum gap between the mirror and the ground to ensure that the actuator does not adhere the substrate (due to molecular force) is computed. It is found that proposed model is able to predict the experimental results more accurately than the previous classic models.

Using Modified Couple Stress Theory to Investigate the Size-Dependent Instability of Rotational Nano-Actuator under Van der Waals Force