تحلیل ارتعاشات آزاد تیر هدفمند دوار باریک‌شوندۀ دو طرفه با استفاده از تئوری اولر-برنولی و روش تبدیل دیفرانسیلی

علوم کاربردی و محاسباتی در مکانیک

مقاله 7، دوره 27، شماره 1 - شماره پیاپی 13، اسفند 1394، صفحه 51-70   

نوع مقاله: مقاله پژوهشی

شناسه دیجیتال (DOI): 10.22067/fum-mech.v27i1.34525

نویسندگان

فرزاد ابراهیمی^* ؛ سمانه دشتی

دانشگاه بین المللی امام خمینی (ره)

چکیده

در این مقاله ارتعاشات آزاد تیر هدفمند دوار باریک‌شوندۀ دو طرفه بررسی شده است. تحلیل ارتعاشات تیر با استفاده از تئوری اولر- برنولی انجام شده است. فرض می شود خواص تیر در راستای ضخامت آن با استفاده از تابع توانی تغییر می کند. معادلات حاکم با استفاده از اصل همیلتون استخراج شده است. فرکانس های طبیعی تیر با استفاده از روش تبدیل دیفرانسیلی به‌دست آمده و اثر ضرایب باریک‌شوندگی، پارامتر های بی بعد سرعت دورانی، شعاع هاب و شاخص جزء حجمی بر فرکانس طبیعی تیر مورد بررسی قرار گرفته است. نتایج حاصل در قالب چندین جدول و شکل ارائه شده و برای صحت‌سنجی، با نتایج کارهای گذشته مقایسه شده است. مقایسۀ انجام‌شده نشان‌دهندۀ این واقعیت است که فرکانس های طبیعی تیر اولر- برنولی دوار باریک‌شوندۀ دو طرفه ساخته شده از مواد هدفمند با استفاده از روش تبدیل دیفرانسیلی با دقت بالایی حاصل می شود. به‌علاوه نتایج حاصل نشان می دهد پارامترهای سرعت دورانی، ضریب باریک‌شوندگی ارتفاعی و شاخص جزء حجمی اثر مهمی بر فرکانس طبیعی این‌گونه تیرها دارند. اثر پارامتر شعاع هاب و ضریب باریک‌شوندگی عرضی نیز قابل چشم‌پوشی می باشد.

کلیدواژه‌ها

ارتعاشات آزاد؛ مواد هدفمند؛ روش تبدیل دیفرانسیلی؛ تیر اولر- برنولی باریک‌شونده

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