نوع مقاله: مقاله پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد، مهندسی مکانیک، دانشگاه صنعتی شریف، تهران

2 استاد، مهندسی مکانیک، دانشگاه صنعتی شریف، تهران

چکیده

در تحقیق حاضر ارتعاشات غیرخطی اجباری ورق‌های نازک دایروی از جنس مواد هدفمند با در نظرگرفتن شرایط مرزی کلاسیک گیردار مورد مطالعه قرارگرفته است. برای واردکردن جملات غیرخطی هندسی ناشی از جابجایی‌های بزرگ ورق در راستای عرضی (به اندازه ضخامت ورق) از روابط کرنش - جابجایی ون‌کارمن، و برای حل معادلات دینامیکی حاکم بر سیستم از روش اغتشاشاتMMS  و مدهای فرضی در دستگاه مختصات قطبی استفاده شده است. خواص مکانیکی در راستای ضخامت ورق بر طبق رابطه توانی از کسر حجمی مواد تشکیل دهنده ماده هدفمند تبعیت می‌کند. نیروی عرضی اعمالی به صورت هارمونیک، به فرکانس نوسان نزدیک به یکی از فرکانس‌های طبیعی نامتقارن سیستم فرض گردیده است. پدیده‌های ارتعاشات غیرخطی مانند پرش و رزونانس داخلی مورد بررسی قرارگرفته و اثرات شرایط مرزی، تغییرات کسرحجمی ماده هدفمند، دامنه و فرکانس نیروی خارجی اعمالی بر رفتار دینامیکی مطالعه شده است. نتایج بدست ‌آمده از این روش با نتایج موجود در کارهای گذشته و در صورت امکان با نتایج نرم‌افزار‌های المان محدود صحت سنجی شده‌اند.

کلیدواژه‌ها

عنوان مقاله [English]

Nonlinear forced vibrations of thin circular functionally graded plates

نویسندگان [English]

  • Ali Ghaheri 1
  • Asghar Nosier 2

1 Department of Mechanict , Sharif Universtiy

2 Department of Mechanict , Sharif Universtiy

چکیده [English]

Abstract Nonlinear forced vibrations of thin functionally graded circular plates under classical clamped boundary conditions are investigated based on the classical plate theory. The von Karman strain-displacement relations are employed to include the geometrical nonlinearity caused by large transverse displacements of the order of the plate thickness. Modal expansion in polar coordinate system along with the perturbation method of multiple scales is used to solve the governing equations. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. Transverse forcing is supposed to be harmonic with the angular frequency near to the natural frequency of one particular asymmetric mode. Nonlinear vibration phenomena such as jump phenomenon and internal resonance are studied and the effects of boundary conditions, power-law distribution, amplitude and frequency of external load on dynamical behavior of circular plate are examined. The validity of results is established by comparison with the existing results in the literature as well as FEM results.  

کلیدواژه‌ها [English]

  • analytical solution
  • Perturbation technique
  • Functionally graded materials
  • von Karman theory

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