تحلیل رشد عدم قطعیت در ارتعاشات آزاد ورق کامپوزیتی نامعین به روش المان محدود تصادفی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 تهران- انتهای امیرآباد شمالی- بعد از پل حکیم- دانشکده علوم و فنون نوین دانشگاه تهران- دفتر معاونت علمی

2 دانشگاه تهران

3 پژوهشگاه فضایی ایران

چکیده

به‌منظور پیش‌بینی‌ قابلیت‌ اطمینان سازههای کامپوزیتی‌ نیاز است‌ عدم قطعیت‌ در پاسخ‌های استاتیکی‌ و دینامیکی‌ این‌ سازهها کمی‌سازی شود. در تاریخچه‌ موضوعی‌ تحقیقی‌ که‌ در آن خواص ورق کامپوزیتی‌ به‌ صورت میدان تصادفی‌ و نه‌ پارامتر تصادفی‌ مدلسازی شده باشد و اثرات آن بر ارتعاشات آزاد ورق مطالعه‌ شده باشد، مشاهده نشد. در این‌ تحقیق‌ خواص فیزیکی‌ و مکانیکی‌ مربوط به‌ ورق کامپوزیتی‌ شامل‌ چگالی‌، مدول کششی‌ و مدولهای برشی‌ در ورق به‌صورت یک‌ میدان تصادفی‌ گوسی‌ در نظر گرفته‌ می‌شود. با در نظر گرفتن‌ تابع‌ خودهمبستگی‌ نمایی‌، میدان تصادفی‌ به‌ روش کارهونن‌-لاو به‌ دو بخش‌ معین‌ و نامعین‌ تجزیه‌ می‌گردد. با فرض تئوری مرتبه‌ اول برشی‌ و تئوری الاستیک‌ خطی‌ کرنش‌های سیستم‌ تعریف‌ شده است‌. انرژی پتانسیل‌ و جنبشی‌ با روش المان محدود استخراج شده است‌. با استخراج معادلات حرکت‌ تصادفی‌ به‌ کمک‌ اصل‌ همیلتون و معادلات اویلر لاگرانژ، فرمولاسیون و روش حل‌ برای حل‌ مسأله‌ معین‌ با نتایج‌ موجود در تاریخچه‌ مقایسه‌ و صحه‌گذاری شده است‌. اثرات عدم قطعیت‌ در خواص بر میزان عدم قطعیت‌ در فرکانس‌ طبیعی‌ سازه با روش مونت‌کارلو مطالعه‌ شده است‌. نتایج‌ نشان می‌دهد، رابطه‌ای خطی‌ بین‌ ضریب‌ تغییرات خواص فیزیکی‌ و مکانیکی‌ و ضریب‌ تغییرات فرکانس‌ طبیعی‌ ورق کامپوزیتی‌ وجود دارد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Uncertainty Propagation Analysis in Free Vibration of Uncertain Composite Plate Using Stochastic Finite Element Method

نویسندگان [English]

  • Mahdi Fakoor 1
  • Hadi Parviz 2
  • Arash Abbasi 3
2 University of Tehran
3 Iranian space research center
چکیده [English]

Material uncertainty is more widespread in composite material than the other engineering materials. This uncertainty makes response of these types of structures to be nondeterministic. In order to predict structural reliability, uncertainty in structural responses must be quantified. There is not a reported research in the literature studying free vibration of composite plate with spatially stochastic material properties. In this research, physical and mechanical properties of composite plate including tensile and shear modulus and density of the plate are modeled as stochastic Gaussian fields. Assuming exponential auto covariance kernels for aforementioned stochastic fields, they are discretized to two parts, including deterministic and stochastic parts employing Karhunen-Loeve theorem. Assuming linear form of strains, mechanical strains are defined applying first order shear deformation theory. Kinetic and potential energy of the composite plate is extracted using finite element formulation. Stochastic finite element formulation is derived employing Hamilton’s principle and Euler-Lagrange and equations are verified with the results in the literature for deterministic case. After verification of formulation, material uncertainty effects on uncertainty of natural frequencies are investigated using Monte Carlo simulation. Results show that there is a linear relation between coefficient of variation of uncertain properties and coefficient of variation of stochastic natural frequencies.

کلیدواژه‌ها [English]

  • Uncertain composite plate
  • stochastic finite element method
  • Karhunen - Loeve theorem
  • Monte Carlo method
  • Free vibration

مراجع

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نشریه مهندسی مکانیک امیرکبیر
دوره 52، شماره 12
اسفند 1399
صفحه 3503-3520

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