بررسی ارتعاشات آزاد ورق قطاعی تابعی مدرج دوبعدی کوپل با پیزوالکتریک مستقر بر بستر الاستیک دوپارامتری با استفاده از روش رایلی ریتز و تئوری مرتبه سوم تغییر شکل برشی

نوع مقاله : مقاله پژوهشی

نویسندگان

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

2 گروه مهندسی مکانیک، دانشگاه اراک، اراک، ایران

چکیده

دراینمقالهارتعاشاتآزادورققطاعیتابعیمدرجدوبعدیکوپلباپیزوالکتریکبرمبنایتئوریمرتبهسومتغییر شکلبرشیمستقربربسترالاستیکدوپارامتریموردبررسیقرارگرفتهاست. تئوریمرتبهسومتغییرشکلبرشیورقبا وجودداشتنمعادلاتپیچیدهتربدلیلدرنظرگرفتنتاثیراتتغییرشکلبرشیعرضیواینرسیدورانیمنجربهحصولنتایج دقیقتریمی‌شود. تغییرخواصورقمدورتابعیدوبعدیبهصورتپیوستهدردوراستایضخامتومحیطدرنظرگرفتهشده استوبرایمدلسازیرفتارورقتابعیدوبعدیازمدلقانونتوانیکسرحجمیاستفادهشدهاست. بهمنظورتعیینپتانسیل الکتریکیلایه‌هایپیزوالکتریکازتوابعسینوسیاستفادهشدهاستبهنحویکهمعادلهالکترواستاتیکیماکسولبوسیلهاین توابعارضامی‌شود. پسازتشکیلفانکشناللاگرانژینبوسیلهتفاضلانرژی‌هایجنبشیوپتانسیلورق،ازاصلهمیلتونو روشریتزبهمنظورتعیینمقادیرفرکانسطبیعیورقاستفادهشدهاست. درادامهپسازاعتبارسنجینتایجبامراجعمختلف برایحالت‌هایگوناگون،تاثیرپارامترهایورقازجملهزاویهقطاعورق،نسبتضخامتبهشعاعورق،ضریبتوانینسبت حجمیوضرایببستربررویفرکانسطبیعیسازهموردبحثوبررسیقرارگرفتهاست.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Free Vibration Analysis of Two-Dimensional Functionally Graded Annular Sector Plates with Piezoelectric Layers Resting on Two-Parameter Elastic Foundation

نویسندگان [English]

  • A. Bakhsheshy 1
  • H. Mahbadi 1
  • K. Khorshidi 2
1 Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 Department of Mechanical Engineering, Arak University, Arak, Iran
چکیده [English]

In this paper, free vibration analysis of two-dimensional functionally graded annular sector plates with two piezoelectric layers on elastic foundation using the Rayleigh-Ritz method is investigated applying the third order shear deformation theory of plates. Despite the existence of more complex equations, the third-order shear deformation theory of plates leads to more accurate results, this is due due to the effects of transverse shear deformation and inertial rotation,.The material properties of the annular plate is graded two-dimensionally in both of the circumferential and thickness directions. The volume fraction power law distribution is used to model the two dimensional functionally graded plate properties. The sinusoidal function is used to determine the electrical potential of the piezoelectric layers. The assumed potential function satisfies the Maxwell electrostatic equations. To obtain the natural frequencies of the plate, the Lagrangian function is defined by subtracting the kinetic and potential energies of the plate and then the Hamilton’s principle and the Ritz method is applied to obtain the natural frequencies of the plate. Finally, the results are validated by various references and the effect of various parameters including the sector angle, ratio of thickness to radius of the plate and foundation coefficients on the natural frequency of the structure has been discussed.

کلیدواژه‌ها [English]

  • Sector plates
  • Natural frequency
  • Rayleigh-Ritz Method
  • Piezoelectric
  • Functionally graded materials

مراجع

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نشریه مهندسی مکانیک امیرکبیر
دوره 51، شماره 1
فروردین و اردیبهشت 1398
صفحه 109-118

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