تحلیل ارتعاشات آزاد تیرهای متخلخل تابعی مدرج روی بستر الاستیک در محیط حرارتی با روش مربعات دیفرانسیلی

نوع مقاله : گرایش دینامیک، ارتعاشات و کنترل

نویسندگان

1 دانشجوی دکتری، دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی واحد شیراز، شیراز، ایران

2 نویسنده مسئول: استادیار، دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی واحد شیراز، شیراز، ایران

3 استادیار، دانشکده مهندسی مکانیک و انرژی، دانشگاه تگزاس شمالی، تگزاس، ایلات متحده آمریکا

4 دانشیار، دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی واحد شیراز، شیراز، ایران

چکیده

در این مقاله ارتعاشات آزاد تیرهای متخلخل تابعی مدرج با شرایط مرزی ساده، روی بستر الاستیک در محیط حرارتی با استفاده از تئوری تغییر شکل برشی مرتبه سوم ردی، موردمطالعه قرار گرفت. خواص مواد به دما وابسته بوده و به‌طور پیوسته در جهت ضخامت تیر و بر اساس مدل توانی توزیع کسر حجمی مواد تشکیل دهنده تغییر می‌کند. توزیع تخلخل یکنواخت در سطح مقطع موردبررسی قرار می‌گیرد. اصل همیلتون برای به دست آوردن معادلات حاکم بر حرکت به کار گرفته شد. به‌منظور گسسته سازی این معادلات، روش مربعات دیفرانسیلی تعمیم‌یافته استفاده‌شده است. در اینجا اثر پارامترهای مختلف از قبیل نوع میدان حرارتی، مقدار اختلاف دما، شاخص قانون توانی، کسر حجمی تخلخل، نسبت لاغری و پارامترهای بستر الاستیک روی فرکانس‌های طبیعی تیر متخلخل تابعی مدرج و برای شرایط تکیه‌گاهی ساده، موردمطالعه قرار گرفت. نتایج علاوه برنشان دادن این تأثیرات بر رفتار ترمومکانیکی تیر، صحت روش عددی مورداستفاده را نیز تأیید می‌نماید.

کلیدواژه‌ها


عنوان مقاله [English]

Analysis of Free Vibrations of Functionally Graded Porous Beams on Elastic Foundation in Thermal Environment Using Differential Quadrature Method

نویسندگان [English]

  • Mahdi Khakpour 1
  • Yousef Bazargan-Lari 2
  • Parham Zahedinejad 3
  • Mohammad Javad Kazemzadeh-Parsi 4
1 Ph.D. Student, Faculty of Mechanical Engineering, Islamic Azad University Shiraz Branch, Shiraz, Iran
2 Corresponding author: Assistant Professor, Faculty of Mechanical Engineering, Islamic Azad University Shiraz Branch, Shiraz, Iran
3 Assistant Professor, Faculty of Mechanical and Energy Engineering, North Texas University, Texas, USA
4 Associate Professor, Faculty of Mechanical Engineering, Islamic Azad University Shiraz Branch, Shiraz, Iran
چکیده [English]

In this paper, the free vibrations of functionally graded porous beams with simple boundary conditions on an elastic foundation in a thermal environment were studied using the theory of third-order shear deformation. The properties of the material are temperature dependent and continuously change in the direction of the thickness of the beam and according to the power law distribution of the volume fraction of the material constituents. The uniform porosity distribution at the cross section is examined. Hamilton's principle was used to obtain the governing equations of motion. In order to discretize these equations, the generalized differential quadrature method has been used. Here, the effect of various parameters such as heat field type, temperature difference, power law index, porosity volume fraction, slenderness ratio and elastic foundation parameters on the natural frequencies of a functionally graded porous beam was studied for simple boundary conditions. The results, in addition to showing these effects on the thermomechanical behavior of the beam, also confirm the accuracy of the numerical method used.

کلیدواژه‌ها [English]

  • Free Vibration
  • Functionally Graded Porous Beams
  • Thermal Environment
  • Elastic Foundation
  • Differential Quadrature Method

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دوره 18، شماره 1 - شماره پیاپی 67
شماره پیاپی 67، فصلنامه بهار
خرداد 1401
صفحه 183-199
  • تاریخ دریافت: 11 تیر 1400
  • تاریخ بازنگری: 10 مهر 1400
  • تاریخ پذیرش: 20 دی 1400
  • تاریخ انتشار: 01 اردیبهشت 1401