نوع مقاله: مقاله پژوهشی

نویسندگان

1 استادیار؛ دانشکده مهندسی مکانیک، دانشگاه اراک، اراک، ایران

2 دانشجوی کارشناسی ارشد، دانشکده مهندسی مکانیک، دانشگاه اراک، اراک، ایران

چکیده

در این مقاله تحلیل ارتعاش آزاد نانو ورق مرکب مستطیلی تابعی هدفمند در محیط حرارتی بررسی شده است. برای به‌دست آوردن فرکانس طبیعی نانو ورق مرکب از تئوری الاستیسیته‌ی غیر محلی بر پایه‌ی تئوری تغییر شکل برشی نمایی استفاده شده است. در تئوری تغییر شکل برشی نمایی، تابع نمایی در راستای ضخامت، برای در نظر گرفتن تاثیرات تغییر شکل برشی عرضی و اینرسی دورانی به‌کار می‌رود. از تئوری الاستیسیته غیر محلی جهت در نظر گرفتن پارامتر مقیاس طول کوچک نانو ورق تابعی هدفمند استفاده شده است. حرارت در سطوح ورق ثابت در نظر گرفته شده است. خواص مواد وابسته به دما و در راستای ضخامت بر اساس قانون توزیع توانی تغییر می‌کند. معادلات حرکت با بکارگیری اصل همیلتون به‌دست می‌آیند. به‌منظور اعتبار سنجی روش حاضر مقایسه‌ای بین نتایج حاصله و نتایج سایر مقالات در دسترس انجام می‌شود. در نهایت تاثیر پارامترهای مختلف از قبیل پارامتر غیر محلی، ضریب نسبت حجمی توانی، نسبت عرض به طول، نرخ ضخامت به طول و دماهای سطح مختلف بر نانو ورق مستطیلی تابعی هدفمند در محیط حرارتی ارایه شده و جزییات مورد بحث قرار گرفته‌اند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Free vibrations analaysis of functionally graded composite rectangular na-noplate based on nonlocal exponential shear deformation theory in thermal environment

نویسندگان [English]

  • Korosh Khorshidi 1
  • Abolfazl Fallah 2
  • Ali Siahpush 2

1 Department of Mechanical Engineering, Arak University, Arak, Iran

2 Department of Mechanical Engineering, Arak University, Arak, Iran

چکیده [English]

In the present study the free vibration analysis of functionally graded composite rectangular nanoplates in thermal environment is investigated. The nonlocal elasticity theory based on the exponential shear deformation theory has been used to obtain the natural frequencies of the nanoplate. In exponential shear deformation theory an exponential functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. Nonlocal elasticity theory is employed to investigate effect of small scale on natural frequency of the functionally graded rectangular nanoplate. The temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction only. Material properties are assumed to be temperature dependent, and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The govering equations are derived by implementing Hamilton’s principle. To show the accuracy of the formulations, present result’s in specific cases are compared with available results in literature and good agreement are seen. Finally, the effect of various parameters such as nonlocal parameter, power law indexes, width to length ratio, the thickness to length ratio, and temperature fields on the natural frequencies of rectangular FG nanoplates are presented and discussed in detail.

کلیدواژه‌ها [English]

  • Nanoplate
  • Functionally graded material
  • Exponential shear deformation theory
  • Thermal environment

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