ارتعاشات غیرخطی پوسته‌ی استوانه‌ای تقویت‌شده به صورت مدرج تابعی با ورقک‌های گرافنی به کمک روش مقیاس چندگانه

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه مهندسی مکانیک، دانشگاه صنعتی قم، قم، ایران

چکیده

در این پژوهش، رفتار دینامیک غیرخطی پوسته‌ی استوانه‌ای تقویت‌شده با ورقک‌های گرافنی دارای توزیع یکنواخت و غیریکنواخت مورد بررسی قرار می‌گیرد. برای این منظور، با در نظر گرفتن تئوری کلاسیک پوسته‌های نازک و بهره‌گیری از مدل غیرخطی فون کارمن در روابط کرنش-جابه‌جایی، ابتدا معادلات حرکت حاکم استخراج شده و خواص مکانیکی پوسته‌ی تقویت‌شده نیز با استفاده از مدل میکرومکانیک هالپین-تسای و قانون اختلاط تعیین می‌شود. سپس معادلات دیفرانسیل جزئی حاکم، به کمک روش گالرکین به معادلات دیفرانسیل معمولی غیرخطی تبدیل شده و در ادامه، این معادلات با روش اغتشاشی مقیاس چندگانه حل می‌گردد. به‌منظور صحت‌سنجی، نتایج به‌دست‌آمده با داده‌های موجود در مراجع و همچنین روش عددی رانگ-کوتا مقایسه می‌شود. در پایان، تأثیر پارامترهای مختلف ماده‌ی هدفمند نظیر تعداد لایه‌ها، الگوهای توزیع ورقک‌های گرافن شامل  UD، FG-X، FG-O  و FG-V و نیز درصد وزنی این ورقک‌ها بر رفتار دینامیک غیرخطی پوسته، در قالب منحنی پاسخ فرکانسی برای تشدید اولیه، بررسی می‌گردد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Nonlinear Vibrations of Functionally Graded Graphene Reinforced Composite Cylindrical Shells Using the Multiple Scale Method

نویسندگان [English]

  • Roham Afshari
  • Nima Mohandesi
  • Mostafa Talebitooti
Department of Mechanical Engineering, Qom University of Technology, Qom, Iran
چکیده [English]

In this research, the nonlinear dynamic behavior of a cylindrical shell reinforced with graphene platelets, examining both uniform and non-uniform distributions of the platelets, is explored. The classical shell theory, complemented by von Karman's nonlinear model for strain-displacement relationships, facilitates the derivation of the governing equations of motion. The mechanical properties of the reinforced shell are ascertained through the Halpin-Tsai micromechanical model and the rule of mixtures. For the transition from partial differential equations to nonlinear ordinary differential equations, the Galerkin method is employed. These resultant equations are subsequently addressed using a multiple scale method. Initial validation of the proposed approach is achieved by comparing the results with the existing literature, and by employing the Runge-Kutta numerical method. Following this validation, the study investigates the impact of various parameters associated with the functionally graded material, such as the number of layers, the distribution patterns of the graphene platelets (including uniform distribution, FG-X, FG-O, and FG-V), and the proportion of these platelets in the composition, all of which significantly influence the nonlinear dynamic behavior of the shell as represented by the response curves for the primary resonance frequency.

کلیدواژه‌ها [English]

  • Nonlinear Vibration
  • Functionally Graded Graphene Platelets
  • Multiple Scale Method
  • Primary Resonance
  • Hapin-Tsai Model

مراجع

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