تاثیر دقت پارامتر مقیاس طول بر فرکانس های طبیعی میکرو ورق مستطیلی متخلخل مرتعش

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه مهندسی مکانیک، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران

چکیده

پارامتر مقیاس طول به عنوان یک فاکتور اساسی نقش مهمی در تقریب مقادیر فرکانس طبیعی میکروساختارها ایفا می‌کند. در این پژوهش با استفاده از پارامترهای مقیاس طول دقیق که اخیرا توسط پژوهشگران در مقیاس آزمایشگاهی اندازه‌گیری شده است، فرکانس‌های طبیعی میکروورق‌های متخلخل محاسبه شده است. با توجه به اینکه ثابت فرض‌نمودن پارامتر مقیاس طول باعث انحراف مقادیر فرکانس طبیعی از مقدار دقیق آن می‌شود، در این تحقیق مقادیر پارامتر مقیاس طول، تابعی از جنس ماده و ضخامت ورق در نظر گرفته شده است. به منظور مدلسازی ساختار مختلخل ورق، از مدل‌های تخلخل پیشنهادی شامل مدل تخلخل یکنواخت، مدل تخلخل غیریکنواخت متقارن و مدل تخلخل غیریکنواخت نامتقارن استفاده شده است. میکروورق نازک درنظرگرفته‌شده و میدان جابجایی بر اساس فرضیات صفحات نازک درنظرگرفته‌شده است. برای تقریب رفتار ورق در ساختار میکرو، مدل غیرکلاسیک تنش کوپل اصلاح‌شده بکار گرفته شده است. توابع حدس به فرم چندجمله‌ای برای ارضا شرایط مرزی مختلف ارائه شده است. حل معادلات پس از محاسبه مقادیر انرژی سیستم به روش عددی رایلی- ریتز انجام گرفته است، و پس از بررسی صحت روند حل انجام شده به وسیله اعتبار سنجی نتایج با مراجع معتبر، تاثیر پارامترهای مختلف ورق در قالب جداول و منحنی بر فرکانس طبیعی سازه مورد ارزیابی قرار گرفته است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

The effect of accuracy of the length scale parameter on natural frequencies of porous rectangular microplate

نویسندگان [English]

  • Ali Bakhsheshy
  • Hossein Mahbadi
Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
چکیده [English]

The length-scale parameter as a primary factor has an important role in the approximation of natural frequencies of micro-structures. Applying the exact length scale parameters which are recently determined by researchers, natural frequencies of porous microstructures are determined. Since the assumption of constant length-scale parameter leads to deviation of natural frequencies from their exact value, this research applies a length scale parameter which is a function of plate thickness and material. To model the porous structure of the microplate, various porous models including evenly porosity mode, unevenly symmetric porosity model, and unevenly asymmetric porosity model are employed. The microplate is assumed to be thin, and classical plate theory is utilized to approximate the displacement field of the microplate. The modified couple stress theory is used to capture the microstructural behavior of the microplate. The trial functions which satisfy the boundary conditions are taken as the polynomial form. Evaluating the energy values of the system, the Rayleigh-Ritz method is employed to solve the governing equations of the system. The results obtained in the present work are validated with data given in the literature search. A parameter study is performed to study the effects of various parameters on the natural frequency of the microplate.

کلیدواژه‌ها [English]

  • porous rectangular microplate
  • Modified Couple Stress Theory
  • length scale parameter
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