تحلیل ارتعاشات پوسته‌های مخروطی ناقص سه‌فازی پلیمر-نانوپلاکت‌گرافنی-الیاف مستقر بر یک بستر الاستیک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه آزاد اسلامی شاهین شهر

2 دانشگاه آزاد اسلامی واحد آباده

چکیده

در این مقاله یک حل نیمه تحلیلی برای مطالعه‌ی ارتعاشات آزاد پوسته‌های مخروطی کامپوزیتی سه‌فازی تقویت‌شده با نانوپلاکت‌های‌ گرافنی1 و الیاف شیشه‌ای، مستقر بر یک بستر الاستیک ارائه می‌شود. پوسته‌ی مخروطی بر اساس تئوری تغییرشکل برشی مرتبه اول2 مدل‌سازی می‌گردد و رفتار بستر الاستیک که پوسته را احاطه کرده است بر اساس مدل پاسترناک3 تخمین زده می‌شود. به منظور محاسبه خواص مکانیکی مؤثر ساختار سه‌فازی پلیمر-نانوپلاکت‌گرافنی-الیاف در کنار قانون اختلاط از مدل هالپین-‌تسای4 و روابط میکرومکانیکی استفاده می‌شود. معادلات حاکم و شرایط مرزی متناظر با بهره‌گیری از اصل هامیلتون5 استخراج می‌شوند، پس از ارائه‌ی یک حل دقیق در راستای پیرامونی پوسته با استفاده از توابع مثلثاتی مناسب، یک حل تقریبی در راستای طولی پوسته با استفاده از ‌روش مربعات دیفرانسیلی6 ارائه می‌شود. فرکانس‌های طبیعی پوسته در مودهای ارتعاشی گوناگون و شکل مودهای متناظر برای شرایط مرزی مختلف شامل ترکیبات مختلفی از لبه‌های گیردار، ساده و آزاد در دو لبه‌ی پوسته استخراج می‌شوند. پس از تأیید همگرایی حل عددی انجام شده در راستای طولی و سنجش میزان اعتبار نتایج ارائه‌شده، تأثیر مشخصات گوناگون بر روی فرکانس‌های طبیعی مورد بررسی قرار می‌گیرد که از آن جمله می‌توان به عدد موج پیرامونی، زاویه نیم‌رأس مخروط، کسر جرمی الیاف، کسر جرمی نانوپلاکت‌های‌ گرافنی و شرایط مرزی در دو لبه‌ی پوسته اشاره نمود. 

کلیدواژه‌ها

عنوان مقاله [English]

Free Vibration Analysis of Polymer/Graphene Nanoplatelet/Fiber Truncated Conical Shells Embedded in an Elastic Foundation

نویسندگان [English]

  • Amir Hossein Yousefi 1
  • hossein amirabadi 2
  • farhad kiani 1
1
2
چکیده [English]

 In this paper, a semi-analytical solution is presented for the free vibration analysis of a three-phase polymer-based truncated conical shell reinforced with Graphene NanoPlatelets (GNPs) and glass fibers, embedded in an elastic foundation. The conical shell is modeled based on the First-order Shear Deformation Theory (FSDT), and the elastic foundation is modeled using the Pasternak model. The effective mechanical properties of the three-phase polymer/GNP/fiber composite are estimated utilizing the rule of mixture, Halpin-Tsai model, and the micromechanical relations. The set of the governing equations and associated boundary conditions are derived using Hamilton’s principle, and are solved analytically in the circumferential direction using trigonometric functions and numerically in the meridional direction via the Differential Quadrature Method (DQM). The natural frequencies and corresponding mode shapes are derived for various boundary conditions, including different combinations of clamped, simply supported, and free edges at both ends of the shell. Convergence of the presented numerical solution is examined, the accuracy of the presented results is confirmed, and the effects of various parameters on the natural frequencies of the shell are investigated including the circumferential wave number, semi-vertex angle of the cone, weight fraction of the fibers, weight fraction of the GNPs, and the boundary conditions.

کلیدواژه‌ها [English]

  • Free vibration
  • Three-phase structures
  • Truncated conical shell
  • Graphene nanoplatelet (GNPs)
  • Pasternak foundation

مراجع

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