نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه آزاد اسلامی واحد علوم و تحقیقات، تهران، ایران

2 دانشگاه خواجه نصرالدین طوسی- تهران-ایران

چکیده

در این پژوهش به بررسی ارتعاشات آزاد ورق دایروی از جنس مواد تابعی در تماس با سیال محدود و غیرقابل تراکم پرداخته شده است. ابتدا معادلات حاکم بر ورق دایروی بر اساس تئوری مرتبه اول تغییر شکل برشی یا تئوری میندلین با در نظر گرفتن اثرات اینرسی دورانی و نیروهای برشی استخراج شده است. برای تقریب جابجایی‌های ورق از توابع پذیرفتنی هارمونیک چبیشف همراه با توابع مرزی استفاده شده است. سپس معادلات حاکم بر نوسان سیال با بهره‌گیری از حل معادله لاپلاس پتانسیل سرعت و ارضای شرایط مرزی حاصل شده است. با استفاده از روش ریتز، فرکانس‌های طبیعی و شکل مودهای ورق دایروی در تماس با سیال بر مبنای انرژی پتانسیل کمینه استخراج شده‌اند. در ادامه، تأثیر پارامترهای مختلف هندسی از قبیل نسبت ضخامت بر شعاع ورق، شرایط مرزی، چگالی سیال، نسبت کسر حجمی ماده تابعی و ارتفاع سیال روی فرکانس‌های طبیعی مورد بررسی قرار گرفته است. به منظور حصول اطمینان از نتایج به دست آمده از حل تحلیلی، فرکانس‌های طبیعی حاصل از ورق دایروی در تماس با سیال در حالت خاص ورق همگن آلومینیومی با نتایج حاصل از آزمایش تجربی مورد مقایسه قرار گرفته است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Hydroelastic vibration analysis of functionally graded circular plate in contact with bounded fluid by Ritz method

نویسندگان [English]

  • shahrouz yousefzadeh 1
  • Aliasghar Jafari 2
  • Alireza Mohammadzadeh 1

1 Islamic Azad University, Science and research branch, Tehran, Iran

2 K. N. Toosi University, Tehran, Iran

چکیده [English]

This study investigates the free vibration of a thick FG circular plate in contact with an inviscid and incompressible fluid. Analysis of the plate is based on First-order Shear Deformation Plate Theory (FSDT) with consideration of rotational inertial effects and transverse shear stresses. Dynamic transverse displacements of the plate are approximated by set of admissible Chebyshev functions which is required to satisfy the geometric boundary conditions. Potential theory together Bernouli’s equation are utilized to obtain the fluid pressure on the free surface of the plate. The governing equation of the oscillatory behavior of the fluid is obtained by solving Laplace equation and satisfying its boundary conditions. The natural frequencies and mode shapes of the plate are determined using Rayleith-Ritz method based on minimizing the Rayleith quotient. The effects of the geometrical parameters such as plate thickness to its radius ratio, boundary conditions, fluid density, volume fraction index, and height of the fluid on natural frequencies and mode shapes are investigated. Comparison of analytically outcome of this study is made with results of the experimental modal test for homogeneous Aluminum plate.

کلیدواژه‌ها [English]

  • Circular plate
  • natural frequency
  • Functionally graded material
  • First order shear deformation plate theory
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