تحلیل ارتعاشات غیر‌خطی الکتروآیروالاستیکی یک عملگر لایه‌ای نانو‌کامپوزیت

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری

2 صنعتی امیرکبیر

چکیده

دینامیک غیر‌خطی و رفتارهای ارتعاشی یک صفحه‌ی ذوزنقه‌ای یکسرگیردار، با یک لایه‌ی نانوکامپوزیت و دو لایه پیزوالکتریک، در این مقاله مورد بررسی قرار گرفته است. این صفحه که به عنوان یک عملگر در ریز‌پرنده‌ها مورد استفاده قرار می‌گیرد، در معرض جریان مادون‌صوت بوده که با کمک نظریه جریان پتانسیل خطی مدل گردیده و تحت تحریک‌های الکتریکی و نیروی خارجی قرار دارد. لایه میانی صفحه توسط نانو‌لوله‌های‌کربنی که به صورت یکنواختی در سرتاسر ضخامت صفحه توزیع شده‌اند، تقویت شده است. معادلات غیر‌خطی صفحه با فرض جابجایی‌های بزرگ ون‌کارمن و با کمک اصل همیلتون استخراج شده و طی نگاشتی، هندسه‌ی صفحه ذوزنقه‌ای از حوزه فیزیکی به حوزه محاسباتی مستطیلی انتقال می‌یابد. همچنین با استفاده از روش گلرکین معادلات دیفرانسیل با دو درجه آزادی و جزء‌های غیر‌خطی مرتبه سه استخراج می‌شود. معادلات با بکارگیری روش مقیاس‌های چندگانه و در حالت تشدید همزمان اولیه و داخلی 1:3 حل گردیدند. در ادامه منحنی‌های پاسخ فرکانسی و زمانی بدست آورده شد و اثرات پارامتر‌های مختلف مانند فشار آیرودینامیک، دامنه‌ی بار‌های عرضی و ولتاژ الکتریکی بر ارتعاشات غیر‌خطی صفحه نازک مورد بررسی قرار گرفت. با توجه به نتایج بدست‌آمده در منحنی پاسخ فرکانسی، رفتار نرم‌شوندگی غیرخطی پیچیده‌ای با دو قله در مد بالاتر مشاهده می‌شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Nonlinear Electro-aero-elastic Vibration Analysis of a Nanocomposite Laminated Trapezoidal Actuator

نویسندگان [English]

  • Marziye Noroozia 1
  • Firooz Bakhtiari-Nejad 2
1 Mechanical Engineering AUT
چکیده [English]

The nonlinear vibration behaviors of a cantilevered piezoelectric carbon nanotube-reinforced composite trapezoidal plate as an actuator in micro air vehicles are considered in this article. The assumption of the uniformly distributed single-walled carbon nanotubes along the thickness is taken into consideration. The plate is exposed to subsonic airflow which is modeled by linear potential flow theory and subjected to combined parametric and external excitations. The large deflection von Karman plate assumptions are applied to derive the governing equations of the motion of the laminated trapezoidal plate by using Hamilton’s principle. Galerkin’s approach combined with proper transformation is formulated and utilized to transform the geometry of the trapezoidal plate into a rectangular computational domain. The nonlinear two-degrees-of-freedom ordinary differential equations with cubic nonlinearities in the case of 1:3 internal resonance and primary resonance are solved by using the multiple scales method. The frequency-response and time-response curves are obtained to analyze the nonlinear dynamic behavior of the plate and study the effects of different parameters such as the amplitudes and frequencies of the excitations and aerodynamic pressure on the nonlinear vibration and dynamic stability of the thin laminated plate. As a result, a complex softening nonlinearity is observed in frequency-response curves.

کلیدواژه‌ها [English]

  • Trapezoidal actuator
  • Combined parametric and external excitations
  • Internal Resonance
  • Subsonic airflow
  • Multiple scales method
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