مجله مهندسی مکانیک

مجله مهندسی مکانیک

بررسی پایداری دینامیکی تیر اولر – برنولی مدرج تابعی و مقطع متغیر با روش ریتز

نوع مقاله : علمی پژوهشی

نویسندگان
1 کارشناسی ارشد، دانشکده فنی و مهندسی، دانشگاه بین المللی امام خمینی (ره)، قزوین
2 استادیار، دانشکده فنی و مهندسی، دانشگاه بین المللی امام خمینی (ره)، قزوین
چکیده
در مقاله‌ حاضر، پایداری دینامیکی تیر اولر - برنولی مدرج تابعی با مقطع متغیر تحت بارمحوری دینامیکی بررسی می ‌شود. مقطع متغیر به‌صورت تابع‌ نمایی و مصالح از نوع مدرج تابعی ترکیبی از آلومینیوم و اکسید زیرکونیوم فرض می ‌شود. در گام اول، معادله دیفرانسیل حاکم با استفاده از روش همیلتون استخراج می ‌گردد. در گام بعدی، شکل ضعیف معادله محاسبه گردیده و از سری چبیشف به ‌عنوان تابع تغییر مکان عرضی و از تابع بولوتین به‌ عنوان سری زمانی استفاده می‌ گردد. سپس ماتریس‌ های سفتی مصالح، هندسی و جرم استخراج می ‌گردد. در نهایت، مقادیر ضریب بار دینامیکی به ‌ازای فرکانس‌ های تحریک مختلف ریشه‌ یابی می ‌شوند. افزایش ضریب تغییرات سطح و ممان اینرسی، ضریب بار استاتیکی بی ‌بعد و توان ماده تابعی سبب کاهش سفتی تیر گردیده و باعث انتقال تغییرات ضریب بار دینامیکی بی ‌بعد به سمت فرکانس‌ های کوچک ‌تر می ‌شود. تمامی نمودارهای ارائه شده در این مقاله بی بعد است و می‌ تواند ملاک طراحی مهندسان برای طراحی تیرهای مدرج تابعی تحت بار محوری دینامیکی قرار گیرد.
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دوره 33، شماره 2 - شماره پیاپی 155
خرداد و تیر 1403
صفحه 30-44

  • تاریخ دریافت 21 آبان 1402
  • تاریخ بازنگری 05 فروردین 1403
  • تاریخ پذیرش 25 فروردین 1403