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.

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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