بررسی تأثیر توزیع نانولوله‌های کربنی تابعی روی فرکانس‌های ورق قطاعی بر روی بستر الاستیک

نویسندگان

1 دانشگاه بوعلی سینا- دانشگاه آزاد

2 دانشگاه آزاد اسلامی، واحد اراک، باشگاه پژوهشگران جوان و نخبگان، اراک، ایران.

3 استاد دانشگاه رازی

4 دانشیار دانشگاه آزاد همدان

چکیده

در این مقاله ارتعاش آزاد ورق گرد قطاعی سوراخ‌دار تابعی هدفمند که با نانولوله‌های کربنی تقویت‌شده‌اند بررسی شده است. توزیع نانولوله‌های کربنی به‌صورت پیوسته و تغییرات تدریجی و هدفمند در راستای ضخامت ورق، به‌صورت کسر حجمی می‌باشد. ورق گرد قطاعی روی بستر الاستیک دو پارامتری وینکلر-پاسترناک قرار گرفته است. معادلات حرکت ورق با استفاده از اصل همیلتون و تئوری بهبودیافته استخراج گردیده است. این معادلات دیفرانسیل کوپل شده با استفاده از بسط سری مثلثاتی توابع تغییر مکان‌ها، به معادلات دیفرانسیل معمولی تبدیل شده و به کمک روش عددی مربعات تفاضلی حل شده‌اند. نتایج به‌دست‌آمده با نتایج دیگران محققان مقایسه و مطابقت بسیار خوبی بین آن‌ها مشاهده‌شده است. درنهایت اثرات پارامترهای مختلف هندسی، توزیع‌های مختلف از نانولوله‌های کربنی در راستای ضخامت، اثر بستر الاستیک و همچنین شرایط تکیه‌گاهی مختلف بر روی فرکانس‌های طبیعی بررسی‌ شده است.

کلیدواژه‌ها


عنوان مقاله [English]

Investigation of Functionally Graded Carbon Nanotube Distribution Effect on the Frequency of Annular Sector Plates on Pasternak Elastic Foundation

نویسنده [English]

  • m n 2
1
2
3
4
چکیده [English]

In this paper, free vibration of functionally graded carbon nanotube annular sector plates is studied. Distribution of carbon nanotubes is continuous and meaningful and gradual changes of materials in the direction of thickness are in the form of volume fraction. Annular sector plate is placed on the Winkler-Pasternak two parameters elastic foundation. The motion equations of plate are derived using the Hamilton principle and the refined plate theory. These coupled differential equations are transformed to ordinary equations using the trigonometric series expansion of space variation functions and then are solved with the help of differential quadrature method. The obtained results are compared with the other researcher’s results and an excellent agreement can be observed between them. Finally, the effects of different geometric parameters, different distributions of carbon nanotubes in the thickness direction, elastic foundation, and also different boundary conditions on the natural frequencies are investigated.

کلیدواژه‌ها [English]

  • functionally graded
  • Carbon nanotube
  • free vibration
  • annular sector plates
  • differential quadrature method
  • Elastic foundation
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