Application of Piezoelectric and Functionally Graded Materials in Designing Electrostatically Actuated Micro Switches

Document Type : Research Paper


Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology


In this research, a functionally graded microbeam bonded with piezoelectric layers is analyzed under electric force. Static and dynamic instability due to the electric actuation is studied because of its importance in micro electro mechanical systems, especially in micro switches. In order to prevent pull-in instability, two piezoelectric layers are used as sensor and actuator. A current amplifier is used to supply input voltage of the actuator from the output of the sensor layer. Using Hamilton’s principle and Euler-Bernoulli theory, equation of motion of the system is obtained. It is shown that the load type (distributed or concentrated) applied to the micro beam from the piezoelectric layer, depends on the shape of the actuator layer (E.g. rectangle, triangular). Finite element method is implemented for evaluation of displacement field in the micro beam and dynamic response of the micro beam under electric force is calculated using finite difference method. Effect of squeeze film damping on pull-in voltage and time-response of the system is considered using nonlinear Reynolds equation. Effect of several parameters such as gain value between piezoelectric sensor and actuator layer, profile of functionally material, and geometry of the system is considered on dynamic behavior of the micro beam especially on pull-in instability. Results are verified for simple cases with previous related studies in the literature and good agreements were achieved. Results indicate that increasing gain value between sensor and actuator enhances stiffness of the system and will raise pull-in voltage. Also, dependency of dynamic properties of the system such as amplitude and frequency of vibration on functionally graded material profile is shown. The material distribution of the functionally graded material is designed in such a way that results in a specific pull-in voltage.


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