بررسی دوپایداری میکروصفحات پیزوالکتریک تحت فشار بر مبنای تئوری تنش‌کوپل بهبودیافته

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه مهندسی مکانیک، دانشگاه حکیم سبزواری، سبزوار، ایران.

چکیده

اخیراً ثابت شده ‌است علاوه بر ریزسازه‌‌های دارای خمیدگی اولیه، میکرو ورق‌های مسطح تحت فشار نیز می‌توانند ناپایداری واجهش را تجربه کنند. با توجه به کاربرد‌های بالقوه‌ی این میکروصفحات در طراحی سنسور‌های فوق حساس، هدف این مقاله بررسی رفتار دوپایدار چنین سازه‌هایی هنگام ترکیب آن‌ها با یک لایه‌ی پیزوالکتریک است. بدین منظور از تئوری تنش‌کوپل بهبود‌یافته به همراه مدل صفحه‌ی غیرخطی کیرشهف استفاده می‌شود. با استفاده از روش گالرکین، معادلات کاهیده شده تعادل و پایداری حاصل می‌گردند. سپس با حل همزمان این معادلات، نقاط بحرانی مسیر تعادل میکرو ورق تعیین می‌گردند. یافته‌‌های حاضر با نتایج موجود در منابع مقایسه و تأیید می‌شوند. در ادامه تأثیر تحریک پیزوالکتریک بر پاسخ دوپایدار سیستم بررسی می‌گردد. نتایج نشان می‌دهند شکل مسیر تعادل و همچنین تعداد و موقعیت نقاط بحرانی آن با اعمال ولتاژ پیزوالکتریک شدیداً تحت تأثیر قرار می‌گیرند. مقاله حاضر برخلاف مطالعات پیشین نشان می‌دهد، اعمال ولتاژ پیزوالکتریک مثبت همواره باعث کاهش آستانه‌ی ناپایداری کشیدگی سیستم نمی‌شود و گاهی اوقات تحت تحریک مقادیر بزرگ فشار دیفرانسیلی، می‌تواند باعث افزایش آن گردد. همچنین نتایج حاکی از آنند که با اعمال ولتاژ پیزوالکتریک مثبت، ناحیه‌ی واجهش منبسط و با اعمال مقادیر منفی، این ناحیه منقبض می‌گردد. نتایج حاضر می‌تواند برای مهندسان صنعت سیستم‌های میکروالکترومکانیکی بسیار مفید باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Investigating Bi-Stability of Pressurized Piezoelectric Micro-Plates Based on the Modified Couple Stress Theory

نویسندگان [English]

  • Maryam Mohammadjani
  • Amir Reza Askari
Department of Mechanical Engineering, Hakim Sabzevari University, Sabzevar, Iran
چکیده [English]

Recently, it has been substantiated that besides initially curved micro-structures, pressurized flat micro-plates can also experience snap-through instability. Given the potential applications of these micro-plates in designing high-sensitive sensors, the present work aims to investigate the bi-stable behavior of such structures when they are integrated with a piezoelectric layer. To this end, the modified couple stress theory together with the geometric nonlinear Kirchhoff plate model are employed. Hiring Galerkin’s method, the reduced governing equilibrium, and stability equations are then achieved. The limit points associated with the micro-plate equilibrium path are then determined through the simultaneous solution of these equations. The present findings are compared and validated by available results in the literature. The influence of the piezoelectric actuation on the bi-stable response of the system is then investigated. The results reveal that the shape of the micro-plate equilibrium path and the number and the position of its limit points can seriously be affected by applying the piezoelectric voltage. Despite the previous studies, the present paper shows that applying positive piezoelectric voltage does not decrease the pull-in threshold of the system all the time and can sometimes increase it when the micro-plate undergoes large differential pressures. Furthermore, the results reveal that applying positive piezoelectric voltages expands the snapping zone while negative ones downsize this region. The present results can be very useful for micro-electromechanical system engineers.

کلیدواژه‌ها [English]

  • Micro-electromechanical system
  • Differential pressure
  • Snap-through instability
  • Piezoelectric materials
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