Abstract Microelectromechanical systems which are the combination of electrical and mechanical systems, are nowadays being used in different industries as actuators and sensors that used extensively in control, mechanical and electrical systems. Microelectromechanical systems for large-scale production capabilities and integration with electronic systems in a wide range of engineering fields including aerospace, medical, automobile manufacturing and information technology have been widely used. Useful features of these devices has led a successful technology in a number of areas of microelectromechanical systems applications, including accelerometers, pressure sensors, microoptics and so on. Important groups of microelectromechanical systems are microresonator that produced in the types of capacitive, magnetic and piezoelectric devices. In this study, a non-linear model is presented for the mechanical behavior of the microresonators considering the large deflection and size dependent theories and will be discussed the static, dynamic behavior and vibration response of microresonator which contains a microbridge with a proof mass of is in the middle. Microresonator is set up under the electrostatic field in such a way that a direct voltage find a certain equilibrium point and then under alternative voltage can be forced to vibrate at a certain frequency which is commonly equal to the natural frequency. Hence the instability and vibration analysis of the system is of most important for performance eva‎luation and parametric design. The electrostatic field due to the direct and alternating voltages applied to the proof mass, vibrates the microresonators. Considering the modified couple stress theory (MCST), geometric nonlinearity and electrostatic mechanism, a developed size dependent model is presented for the dynamic motion of electrostatically actuated microresonators using extended Hamilton principle. Using a model approximation i.e. Galerkin method, the governing equations of static and oscillatory motions are reduced and the resultant equation is solved by analytical (multiple scale method) and numerical methods. Analytical and numerical results are absolutely in accordance with each other. In reviewing the results, will be discussed the effects of various parameters related to system design including midplane stretching and size dependent effects. The effects of the midplane stretching of the resonator, fringing field and size effect on the instability, the natural frequency and amplitude vibration of the system are investigated. Results show that the midplane stretching and size dependent effects have significant impact on the vibration behavior and instability of the microresonators which have thickness less than six times of the material length scale parameter.

مهدي مجاهدي، مسعود رهايي فرد