مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

اثرات دمایی بر ارتعاشات آزاد نانوتیرهای خمیده تابعی مدرج تیموشنکو روی بستر کشسان وینکلر- پسترناک

نوع مقاله : پژوهشی کیفی

نویسندگان
گروه مهندسی مکانیک، دانشکده مهندسی، دانشگاه زنجان، زنجان، ایران
چکیده
در این مقاله اثرات بارگذاری دمایی و بستر کشسان وینکلر- پسترناک بر ارتعاشات نانوتیر خمیده تابعی مدرج مورد مطالعه قرار گرفته است. فرضیات موجود بر مبنای تئوری تنش کوپل اصلاح‌شده و مدل تیر تیموشنکو توسعه داده شده است. توزیع مواد سازنده در راستای ضخامت پیوسته بوده و به‌واسطه تغییر شاخص گرادیان در کسر حجمی، شیب توزیع مواد در این راستا توصیف شده است. به کمک اصل همیلتون معادلات حاکم و شرایط مرزی به‌دست‌آمده‌اند. با تحلیل نتایج کمی و کیفی در جداول و شکل‌ها، نحوه اثرات پارامترهای مؤثر هندسی و ترموفیزیکی نظیر شاخص گرادیان، نسبت بی‌بُعد طول به ضخامت، اختلاف دمای یکنواخت، نسبت ضخامت به پارامتر مقیاس طولی و زاویه کمان نانوتیر خمیده تابعی مدرج روی فرکانس طبیعی در مدهای مختلف ارتعاشی تفسیر شده است. با اعتبارسنجی همپوشانی خوبی بین نتایج حاضر و مطالعات قبلی به دست آمد. با بررسی نتایج روشن می‌شود که اعمال بارگذاری دمایی سبب افزایش حساسیت فرکانس طبیعی به تغییرات پارامترهای مذکور و همچنین بزرگترشدن دامنه تغییرات آن می‌شود. همچنین لحاظکردن ضریب بستر پسترناک باعث تغییر رفتار فرکانس طبیعی به تغییرات دمایی می‌شود.
کلیدواژه‌ها

موضوعات


عنوان مقاله English

Thermal Effects on Free Vibration of Functionally Graded Curved Timoshenko Nanobeams Resting on Winkler–Pasternak Elastic Foundation

نویسندگان English

I. Ghoytasi
O. Rahmani
Mechanical Engineering Department, Engineering Faculty, University of Zanjan, Zanjan, Iran
چکیده English

In this paper, the effects of unified temperature loading and Winkler-Pasternak elastic foundation on the vibration of functionally graded curved nanobeam have been studied. The proposed model is based on the modified couple stress theory and the Timoshenko beam model. The continuous distribution of material along the thickness of functionally graded curved nanobeam is achieved by changing the gradient index in the volume fraction. The governing equations and related boundary conditions are obtained using the Hamilton principle. By analyzing the quantitative and qualitative results in the tables and figures, influences of geometrical and thermo-physical parameters such as gradient index, aspect ratio, unified temperature difference, the ratio of thickness to length scale parameter and arc angle of functionally graded curved nanobeam on the natural frequency for different vibration mode have been interpreted. There is an excellent agreement between the present results and the results of the previous works. Applied temperature loading increases the sensitivity of the natural frequency to the changes in the aforementioned parameters and also increases the range of its changes. Also, applying the Pasternak elastic foundation changes the behavior of the natural frequency to the temperature changes.

کلیدواژه‌ها English

Functionally Graded Curved Nanobeam
Thermal buckling
Free vibration
Modified couple stress
Winkler–Pasternak Elastic Foundation
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