Influence of optical property contrast on the critical distribution of electrostatic torques in double-beam torsional Casimir actuators: Non-linear actuation toward chaotic motion

Here, we discuss how to achieve the stable actuation of a double beam torsional micro-actuator over the largest possible displacement of the moving component under the influence of Casimir and electrostatic torques, when the rotating component is constructed from different materials. The main part of this study is devoted to finding the optimal distribution of the electrostatic torque between the left and right sides of the micro-actuator to reach the maximum stable operation of the device. The latter is manifested by switching from homoclinic to heteroclinic orbits in the phase portraits. Indeed, the bifurcation curves and the phase portraits have been employed to show the sensitivity of the critical distribution of the electrostatic torque, beyond which the device does show stable performance, on the contrast of the optical properties of the moving component and the applied voltage in a conservative autonomous system. Moreover, for driven systems, the Melnikov function approach and the Poincare portraits are used to study the presence of chaotic motion, which eventually leads to stiction. It is shown that the application of the optimal distribution of the electrostatic torque can significantly decrease the possibility of chaotic motion, and at this optimal level, the threshold curves reveal less difference between systems with different optical contrast.

Automated summary

This study discusses the stable actuation of a double beam torsional micro-actuator and focuses on finding the optimal distribution of electrostatic torque for maximum stable operation. The analysis shows the sensitivity of torque distribution on the optical properties of the moving component and the applied voltage. It is also demonstrated that applying the optimal torque distribution can reduce the possibility of chaotic motion and minimize the difference between systems with different optical contrast.