Abstract




 
   

IJE TRANSACTIONS C: Aspects Vol. 30, No. 12 (December 2017) 1911-1918    Article in Press

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  STABILIZATION OF ELECTROSTATICALLY ACTUATED MICRO-PIPE CONVEYING FLUID USING PARAMETRIC EXCITATION
 
B. Abbasnejad, R. Shabani and G. Rezazadeh
 
( Received: March 24, 2017 – Accepted in Revised Form: September 08, 2017 )
 
 

Abstract    This paper investigates the parametric excitation of a micro-pipe conveying fluid suspended between two symmetric electrodes. Electrostatically actuated micro-pipes may become unstable when the exciting voltage is greater than the pull-in value. It is demonstrated that the parametric excitation of a micro-pipe by periodic (ac) voltages may have a stabilizing effect and permit an increase of the steady (dc) component of the actuation voltage beyond the pull-in value. Mathieu type equation of the system is obtained by applying Taylor series expansion and Galerkin method to the nonlinear partial differential equation of motion. Floquet theory is used to extract the transition curves and stability margins in physical parameters space (Vdc-Vac). In addition, the stability margins are plotted in flow velocity and excitation amplitude space (u-Vac space). The results depict that the micro-pipe remains stable even if the flow velocity is more than the critical value for a certain dc voltage. For instance, in absence of the (ac) component, it is shown that pull-in voltages associated to critical velocities 3 and 6 are 14.06 and 5.4 volt, respectively. However, transition curves show that superimposing an (ac) component with forcing frequency Ω=10 increases the pull-in voltage beyond these values. Furthermore, for the present pull-in voltages the critical velocities 3 and 6 could be increases with imposing some (ac) component. These results are discussed in detail in simulation results section where the transion curves are ploted quantitatively.

 

Keywords    Electrostatically actuated micro-beam, Micro-pipe conveying fluid, Dynamics, Pull-in instability, Parametric oscillation, Floquet theory

 

چکیده    در این مقاله، پایداری یک میکرولوله حامل سیال در شرایط تحریک پارامتریک مورد بررسی قرار گرفته است. که این میکرولوله حامل سیال به صورت متقارن در بین دو الکترود از نوع تحریک الکتروستاتیک قرار دارد. این میکرولوله که تحت تحریک الکتروستاتیک قرار دارد، در شرایطی که ولتاژ تحریک بزرگتر از ولتاژ ناپایداری استاتیکی باشد، ناپایدار میگردد. با اضافه کردن ولتاژ متناوب به ولتاژ ثابت و با به کاربردن سری تیلور و روش گلرکین، معادله حاکم بر سیستم که به فرم معادله ماتیو میباشد، استخراج شده است. با استفاده از تئوری فلوکه و با تغییر پارامترهاي تحریک سیستم نظیر اندازه ولتاژ ثابت و دامنه ولتاژ تناوبی منحنی هاي گذر و نواحی پایدار میکرولوله مشخص شده اند. بعلاوه منحنی های گذر و نواحی پایدار با تغییر سرعت سیال و دامنه ولتاژ هارمونیک نیز به دست آمده اند. . نتا یج نشان میدهند که با افزودن یک مولفه هارمونیک میتوان ولتاژ ناپایداري سیستم را افزایش داده و به مقدار بالاتر از ناپایداري استاتیکی نیز رساند. نتایج به دست آمده براي نقاط خاص به صورت عددي نیز حل شده و پایداري سیستم به صورت موردي بررسی شده است. به عنوان مثال در غیاب ولتاژ هارمونیک، اندازه ولتاژ ناپایداری سیستم به ازای سرعت های بحرانی 3و 6 به ترتیب 06/14و 4/5 ولت می باشد. در صورتیکه منحنی های گذر نشان می دهند که با افزودن مولفه هارمونیک به ولتاژ اعمالی با فرکانس تحریک Ω=10، ولتاز ناپایداری را می توان به اندازه قابل توجهی افزایش داد. علاوه بر این، نتایج نشان می دهند که سرعتهای بحرانی 3و6 نیز به ازای ولتاژهای ناپایداری متناظر، با اعمال ولتاژ هارمونیک افزایش می یابند. تمامی این نتایج به تفصیل در متن مقاله در قسمت نتایج توضیح داده شده اند.

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