Abstract    This paper addresses the static and dynamic stabilities of a parametrically excited torsional micro-actuator. The system is composed of a rectangular micro-mirror symmetrically suspended between two electrodes and acted upon by a steady (dc ) while simultaneously superimposed to an (ac ) voltage. First, the stability of the system subjected to a quasi-statically applied (dc ) voltage is investigated, where the pull-in instability, equilibrium positions, and bifurcation points of the system are determined. Then by superimposing an (ac) voltage and extracting a Mathieu type governing equation the effects of (ac ) component on the stability of the system is investigated. By varying excitation parameters (steady (dc) voltage and time-dependent amplitude of (ac ) excitation), transition curves and the stability margins of the micro-mirror are demonstrated. Theoretically obtained margins are checked by means of numerical simulations. The results show that superimposing the harmonic (ac ) component could have a stabilizing effect and allow an increase of the steady (dc ) component beyond the pull-in value. The obtained results could be used in design of micro-actuators.

Keywords    MEMS, Micro-mirror, Electrostatic actuation, Parametric oscillation, Perturbation method

چکیده    در این مقاله پایداری استاتیکی و دینامیکی یک میکرو آینه در شرایط تحریک پارامتریک مورد بررسی قرار گرفته است. سیستم مورد نظر شامل یک میکرو آینه بوده که بصورت متقارن در بین دو الکترود از نوع تحریک الکترو استاتیک قرار گرفته و بصورت همزمان توسط یک ولتاژ ثابت و یک ولتاژ هارمونیک تحریک می گردد. در ابتدا با اعمال ولتاژ ثابت پایداری استاتیکی سیستم مورد بررسی قرار گرفته و ولتاژ ناپایداری، نقاط تعادل و نقاط دوشاخگی سیستم استخراج شده اند. سپس با اضافه کردن ولتاژ متناوب به ولتاژ ثابت معادله حاکم بر سیستم که بفرم معادله ماتیو می باشد استخراج شده و پایداری سیستم مورد بررسی قرار گرفته است. در ادامه با تغییر پارامترهای تحریک سیستم نظیر اندازه ولتاژ ثابت و دامنه ولتاژ تناوبی منحنی های گذر و نواحی پایدار میکرو آینه مشخص گردیده اند. نتایج بدست آمده از روش اغتشاشات برای نقاط خاص بصورت عددی نیز حل شده و پایداری سیستم بصورت موردی بررسی شده است. نتا یج بدست نشان می دهند که با افزودن یک مولفه هارمونیک می توان ولتاژ ناپایداری سیستم را افزایش داده و به مقدار بالاتر از ناپایداری استاتیکی نیز رساند. منحنی هار گذر و نواحی پایدار بدست آمده می توانند در طراحی و ساخت میکرو آینه ها بکار گرفته شوند.

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