نویسندگان

1 دانشگاه رازی کرمانشاه

2 دانشگاه آزاد اسلامی، واحد اراک

3 دانشگاه آزاد اسلامی، واحد همدان

چکیده

در این مقاله ارتعاش آزاد ورق دایره‌ای سوراخ‌دار تابعی هدفمند که با نانولوله‌های کربنی تقویت شده‌اند بررسی شده است. توزیع نانولوله‌های کربنی به‌صورت پیوسته و تغییرات تدریجی و هدفمند مواد در راستای ضخامت ورق، به‌صورت کسر حجمی است. با توجه به در‌نظر گرفتن تغییرات خطی و غیرخطی ضخامت ورق دایره‌ای در راستای شعاع و نیز با توجه به تابع درنظر گرفته ‌شده برای ضخامت، ضخامت ورق می‌تواند به‌صورت مقعر یا محدب باشد. همچنین معادلات حرکت ورق با استفاده از تئوری تغییر شکل برشی مرتبه سه استخراج شده است. این معادلات یک‌سری معادلات دیفرانسیل درگیر شده هستند که با استفاده از بسط سری مثلثاتی توابع تغییر مکان‌ها، به‌طوری‌ که شرط تقارن محوری را برآورده کند، به معادلات دیفرانسیل معمولی تبدیل می‌شود که حل دقیق آنها بسیار مشکل است به‌همین دلیل از روش عددی تفاضل مربعات برای حل این معادلات استفاده‌ شده است. نتایج به‌دست ‌آمده با نتایج دیگر محققان مقایسه و مطابقت بسیار خوبی بین آنها مشاهده ‌شده است. در نهایت اثرات پارامترهای مختلف هندسی و همچنین درصد کسر حجمی مختلف از نانولوله‌ها برروی فرکانس‌های طبیعی بررسی‌ شده است.

کلیدواژه‌ها

عنوان مقاله [English]

Free Vibration of Functionally Graded Variable Thickness Carbon Nanotube Annular Plates

نویسندگان [English]

  • M. H. Yas 1
  • M. Nejati 2
  • S. S. Jafari 3

چکیده [English]

In this paper, free vibration of carbon nanotube-reinforced functionally graded circular plates with hole has been
investigated. Distribution of carbon nanotubes are continuous and the gradual and graded changes of materials through the
plate thickness are considered as volume fraction. Considering the linear and non-linear variation of circular plates through the
radial direction and also considering the proposed function for the thickness, the plate thickness can be convex or concave.
Moreover, the motion equations of plate were obtained based on the third-order shear deformation theory. These equations are
coupled differential equations which can convert Ordinary Differential Equations (ODE) using the Trigonometric series
expansion of displacement fields such that they satisfy the axial symmetry condition. Solving the converted ODE equations is too
difficult. For this reason, the differential quadrature method is employed to solve these equations. The obtained results are
compared with the results reported by other researchers and an excellent agreement is observed between them. Finally, the effects
of different geometric parameters as well as different volume fracture of nanotubes on natural frequency have been studied.

کلیدواژه‌ها [English]

  • Functionally graded materials
  • carbon nanotube
  • Free vibration
  • Circular plates with hole
  • differential quadrature method
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