تحلیل فرکانسی تیرهای متخلخل ترک‌دار مدرج تابعی روی بستر الاستیک با استفاده از تئوری برشی مرتبه‌سوم ردی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی مکانیک، واحد شیراز، دانشگاه آزاد اسلامی، شیراز، ایران

2 گروه مهندسی مکانیک، دانشگاه آزاد اسلامی، شیراز، ایران

چکیده

در این مقاله، تحلیل فرکانسی تیرهای متخلخل ترک‌دار مدرج تابعی روی بستر الاستیک بر اساس تئوری مرتبهسوم تغییر شکل برشی ردی بررسی می‌شود. مشخصات مکانیکی مواد انتخابشده به‌طور پیوسته در جهت ضخامت تغییر می‌کنند. تغییرات خواص مکانیکی بر اساس مدل قانون نمایی تعیین می‌شود. با بهکارگیری تئوری مرتبهسوم تغییر شکل برشی و با اعمال اثر بستر الاستیک خطی، با استفاده از اصل همیلتون، معادلات دیفرانسیل حاکم بر مسئله حاصل می‌شود. با‌توجه‌به ‌پیچیدگی حل بستهای این معادلات، معادلات دیفرانسیل حاکم با فرض شرایط مرزی از نوع تکیهگاه مختلف، به‌کمک روش مربعات دیفرانسیلی تعمیمیافته حل می‌شوند. به‌منظور صحتسنجی، نتایج این تحقیق با نتایج سایر مقالات مقایسه میشود. این بررسی نشان می‌دهد که اختلاف بین نتایج این مقاله با نتایج سایر مقالات ناچیز است. در نهایت اثر پارامترهای هندسی و شاخص نمایی خواص مواد، موقعیت و عمق ترک لبه، بستر الاستیک و تخلخل روی فرکانس طبیعی تیرهای مدرج تابعی ارزیابی می‌شود. نتایج این مقاله و تأثیرات این پارامترها میتواند در طراحی بهینۀ تیرهای مدرج تابعی و در تکنیکهای پیشبینی، کشف و پایش ترک استفاده شود.  

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Frequency Analysis of Cracked Porous Functionally Graded Beams on Elastic Foundation using Reddy Third Order Shear Deformation Theory

نویسندگان [English]

  • Mohammad Amin Forghani 1
  • yousef bazarganlari 2
  • Parham Zahedinejhad 1
  • Mohammad Javad Kazemzadeh Parsi 1
1 Department of Mechanical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran
2 Department of Mechanical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran
چکیده [English]

In this paper, Frequency analysis of cracked porous functionally graded beams which are resting on elastic foundation based on reddy third order shear deformation theory is studied. Mechanical property gradients defined in accordance with model of exponential law. Governing equations obtained with the aid of third order shear deformation theory and by considering elastic foundation effects within hamilton’s principle. Due to complicating closed form solution of equations, differential equations solved utilizing Generalized Differential Quadrature Method by considering various end conditions. In order to validate the results, comparisons are made with solutions which are available for other papers. This study shows that the difference between the results of this paper and the results of others is negligible. Finally the effects of geometrical parameters, exponential law indexes, crack location and depth, elastic foundation and porosity on natural frequencies of functionally graded beams are studied. The results of this paper and effects of these parameters can be used in the optimum design of functional graded beams and crack prediction, detection and monitoring techniques.

کلیدواژه‌ها [English]

  • frequency analysis
  • Exponential FGM
  • Edge Crack
  • Porous
  • Winkler Pasternak
  • Third Order Reddy Theory
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