مطالعه ارتعاش آزاد پوسته ‌‌استوانه‌ای چرخان از جنس هسته متخلخل‌‌تقویت‌شده و رویه‌ مگنتوالکتروالاستیک با پارامترهای عدمقطعیت در محیطحرارتی

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه مهندسی مکانیک، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران

چکیده

در این پژوهش تحلیل ارتعاش آزاد برای یک پوسته استوانه‌ای دولایه دوار به کمک تئوری مرتبه اول برشی انجام شده است. این پوسته متشکل از لایه داخلی مدرج متخلخل و تقویت‌شده با گرافن و رویه مگنتوالکتروالاستیک بوده و تحت اثر محیط حرارتی قرار دارد. شرایط مرزی دو انتهای پوسته را بدلیل وجود یاتاقان‌هائی که از حرکت عرضی جلوگیری می‌کنند می‌توان بصورت دوسر مفصل درنظرگرفت. در ابتدا، فرکانس طبیعی مودهای پیش‌رونده و پس‌رونده ارتعاش آزاد پوسته دوار کامپوزیتی با خواص کاملا معین محاسبه شده و با نتایج سایر مقالات صحت‌سنجی شده است. سپس تاثیر سرعت دورانی، عدد مود، تغییردما، میزان تخلخل و کسرجرمی گرافن بر نتایج مورد بررسی قرار گرفته است. سپس این مطالعه به دنبال بررسی تاثیر عدم‌قطعیت‌ها در خواص لایه مگنتوالکتروالاستیک بر ارتعاش آزاد پوسته استوانه ای دوار و در معرض پتانسیل‌های الکتریکی و مغناطیسی است. در این حالت عدم قطعیت‌های مدول الاستیک، ضریب پیزوالکتریک و پیزومغناطیس لایه هوشمند، با استفاده از عدد فازی متقارن گوسی مرتبط می‌شوند. معادلات حاکم برای ارتعاش آزاد مدل نامعین با ترکیب اصل همیلتون و فرم پارامتری دوگانه اعداد فازی به‌دست می‌آیند؛ سپس فرکانس‌های طبیعی مدل‌ نامعین با استفاده از رویکرد ناویر محاسبه می‌شوند. ارتعاشات آزاد نیز با محاسبه محدوده فرکانس‌ طبیعی در رابطه با پارامترهای نامعین مختلف بررسی شده‌اند. نتایج عددی نشان داده است که وجود تخلخل فرکانس‌های طبیعی را افزایش می‌دهد. در سرعت دوران صفر، دوبرابر کردن میزان تقویت‌کننده گرافنی منجر به افزایش 21% ، 26% و 33% به ترتیب در فرکانس مودهای اول، دوم و سوم شده است؛ در حالی که در سرعت دورانی بیشینه، دوبرابر کردن گرافن تقویتی منجر به افزایش 14% ، 4/5% و 3/3% به ترتیب در فرکانس مودهای اول، دوم و سوم شده است. در مورد خواص دارای عدم قطیت نیز،  محدوده فرکانس طبیعی با افزایش پتانسیل الکتریکی اندکی کاهش یافته است اما با افزایش پتانسیل مغناطیسی به‌شدت افزایش داشته است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Free Vibration analysis of a rotating cylindrical shell made of FG-GPLR porous core and MEE face with uncertain parameters in thermal environment

نویسندگان [English]

  • Mohsen Khanahmadi
  • Armen Adamian
  • Ahmad Hosseini-Sianaki
Department of Mechanic, central Tehran Branch, Islamic Azad University, Tehran, Iran
چکیده [English]

In this study, free vibration analysis of a rotating composite double-layer cylindrical shell has been carried out using first-order shear deformation theory. The shell is made of a thin magneto-electroelastic (MEE) top layer bonded to the functionally graded graphene platelet reinforced (FG-GPLR) porous layer and is subjected to the thermal environment. The two ends of the shell can be considered as pinned boundary conditions due to the presence of bearings that prevent transverse movement. At first, natural frequencies of the forward and backward modes for the rotating composite shell were obtained and verified by the literature results. Then the effect of rotational speed, mode numbers, temperature change, porosity and GPLs mass fraction on the frequencies were investigated. This study then seeks to investigate the effect of uncertainties in the MEE layer properties on the free vibration of a rotating composite shell exposed to electric and magnetic potentials. In this case, the uncertainties in the elastic modulus, piezoelectric and piezomagnetic coefficient of the smart layer, are introduced using a symmetric Gaussian fuzzy number. The governing equations for the uncertain system are obtained by combining Hamilton's principle and the dual parametric form of fuzzy numbers; Then the natural frequencies of the uncertain model are calculated using Navier's approach. Free vibration is also investigated by obtaining the natural frequency borders with respect to the various uncertain parameters. The results have shown that the porosity increased the frequencies. In the case of uncertain properties, with increasing of the electric potential, the frequency bounds decreased slightly, but they increased intensely with increasing of the magnetic potential.

کلیدواژه‌ها [English]

  • Rotating Composite Cylindrical Shell
  • Magneto-Electro-Elastic Layer
  • FG-GPLR Porous Material
  • Natural Frequency
  • Uncertain Parameters
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