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

نوع مقاله : مقاله پژوهشی

نویسندگان

• فرزاد ابراهیمی
• سمانه دشتی

دانشگاه بین المللی امام خمینی (ره)

10.22067/fum-mech.v27i1.34525

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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عنوان مقاله [English]

Free Vibration Analysis of Functionally Graded Rotating Double Tapered Beam by using Euler-bernoulli Beam Theory and Differential Transform Method

نویسندگان [English]

• farzad ebrahimi
• Samanaeh Dashti

ikiu

چکیده [English]

In this study, the free vibration analysis of a functionally graded rotating double tapered beam is performed. The analysis is based on Euler-Bernoulli beam theory. The Material properties of the beam vary continuously in the thickness direction according to the power-law function. The governing differential equation of motion is derived using the Hamilton’s principle. Natural frequencies are obtained using differential transformation (DTM) technique. The effects of the taper ratios, nondimensional rotational speed, nondimensional hub radius and material volume fraction index on the natural frequencies are discussed. Numerical results are tabulated in several tables and figures. To verify the present analysis, the results of this study are compared with the available results from the existing literature. It is shown that the natural frequencies of a functionally graded rotating double tapered Euler-Bernoulli beam can be obtained with high accuracy by using DTM. It was observed that nondimensional rotational speed, height taper ratio and power-law exponent significantly affect the natural frequency. The effects of hub radius and breadth taper ratio on the natural frequencies are negligible.

کلیدواژه‌ها [English]

• Free Vibration
• functionally graded material
• Differential Transform Method
• Tapered Euler- Bernoulli beam

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