پیش بینی و کنترل آشوب در میکرو صفحه مستطیلی غیرخطی بر روی بستر الاستیک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی مکانیک، دانشکده مهندسی، دانشگاه صنعتی قوچان، قوچان، ایران

2 دانشجوی کارشناسی ارشد، مهندسی مکانیک، دانشگاه صنعتی قوچان، قوچان، ایران

چکیده

در این پژوهش، دینامیک غیرخطی میکروصفحه غیرکلاسیک کیرشهف تحلیل، محدوده رفتار آشوبناک پیش بینی و با طراحی کنترلر مقاوم تطبیقی فازی، کنترل می‌شود. معادله حاکم بر میکروصفحه بر روی بستر الاستیک غیرخطی، با درنظر گرفتن غیرخطی هندسی فون-کارمن و براساس تئوری تنش کوپل اصلاح شده، با استفاده از اصل جابجایی مجازی استخراج می‌گردد. معادله مقدار ویژه حاصل برای شرایط مرزی ساده حل شده و نتایج بدست آمده اعتبارسنجی می‌گردد. در گام بعد، با فرض تحریک هارمونیک مود اول، روش گلرکین بکار برده می‌شود و معادله ارتعاشات اجباری میکروصفحه بدست می‌آید. سپس آستانه آشوب با صرف نظر از برهم کنش مودها تحلیل می‌گردد. مدارهای هموکلینیک سیستم بدون اغتشاش رسم شده و برخورد منیفلدهای پایدار و ناپایدار که معیاری برای پیش بینی آشوب است، با استفاده از روش ملنیکف بررسی می‌شود. همچنین، با استفاده از روش عددی حداکثر نمای لیاپانوف، آشوب وابسته به ابعاد، به‌صورت موضعی شناسایی می‌گردد. نمودارهای صفحه فاز، نگاشت پوانکاره و پاسخ زمانی برای مقادیر مختلف نسبت ابعادی رسم شده و تاثیر چشمگیر ابعاد در رفتار آشوبناک میکروصفحه نمایش داده می‌شود. در ادامه، با طراحی کنترلر مقاوم تطبیقی فازی، ارتعاشات آشوبناک به کلی از سیستم حذف می‌شود و کنترلر مقاوم تطبیقی فازی به عنوان یک روش کارآمد برای کنترل آشوب در این سیستم‌ها معرفی می‌گردد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Prediction and Control of Chaos in Nonlinear Rectangular Micro-Plate on the Elastic Foundation

نویسندگان [English]

  • atieh andakhshideh 1
  • Hossien Karamad 2
1 Department of Mechanical Engineering, Quchan University of Technology, Quchan, Iran
2 Department of Mechanical Engineering, Quchan University of Technology, Quchan, Iran
چکیده [English]

In this study, nonlinear dynamics of non-classical Kirchhoff microplate is analyzed and chaotic behavior is predicted and controlled by designing the robust adaptive fuzzy controller. Virtual displacement principle is employed to derive the governing equation of micro-plate resting on a nonlinear elastic foundation. In the governing equation, von-Karman geometric nonlinearity and couple stress theory are considered. Then eigenvalue governing equation is solved for fully simply supported boundary conditions and results are validated. In the next step, considering harmonic excitation of the first mode, the micro-plate forced vibration equation is derived using the Galerkin method. Regardless of modal interaction, the chaos threshold is then investigated. Homoclinic orbits of the unperturbed system are plotted and stable and unstable manifold transversely cut that is criteria to predict chaos according to Melnikov’s method are studied. Using the maximum Lyapunov exponents numerical method, size-dependent chaos is also locally identified. Phase portrait, Poincare mapping and time response are plotted for different values of size ratios and the significant effect of size on the chaotic behavior of micro-plats is presented. Subsequently, designing the robust adaptive fuzzy controllers, chaotic vibrations are completely eliminated from the system and the robust adaptive fuzzy controller is introduced as an effective method for controlling chaos in these systems.

کلیدواژه‌ها [English]

  • Nano-electromechanical systems
  • Robust adaptive fuzzy controller
  • Couple stress theory
  • Kirchhoff micro-plates
  • chaos
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