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پاسخ تحلیلی ارتعاشات آزاد میرای تیر ترکدار با معادلات حرکت چند مودی کوپل | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 11، دوره 52، شماره 1، فروردین 1399، صفحه 155-172 اصل مقاله (2.28 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2018.13957.5762 | ||
| نویسندگان | ||
| موسی رضائی* 1؛ وحید شاطریان القلندیس2 | ||
| 1دانشگاه تبریز | ||
| 2گروه مهندسی مکانیک، دانشکده مهندسی مکانیک، دانشگاه تبریز | ||
| چکیده | ||
| در این مقاله، ارتعاشات چند مودی آزاد تیر با ترک خستگی تحت شرایط اولیه دلخواه مطالعه شده است. اعمال شرایط اولیه دلخواه باعث تحریک همزمان چند مود ارتعاشی تیر می شود. برای تحلیل مسأله، با در نظر گرفتن گشتاور خمشی تیر در محل ترک، رابطه ای برای تعیین میزان باز شدگی آنی ترک به صورت تابعی چندهارمونیک از زمان ارائه می شود. تابع توصیف کننده وضعیت آنی ترک در مجموعه معادالت مودال توصیف کننده ارتعاشات تیر ترکدار ظاهر شده و سبب کوپل شدن معادالت می شود. این معادالت با استفاده از روش اغتشاشات حل و پاسخ تحلیلی ارتعاش چند مودی تیر ترکدار به تحریک اولیه دلخواه به دست می آید. سپس پاسخ ارتعاشی تیر در سه حالت: تحریک مود اول، تحریک همزمان مودهای اول و دوم و تحریک همزمان مودهای اول تا سوم به دست آمد. نتایج نشان می ً دهد که با تحریک صرفا در مود اول، مؤلفههای هارمونیک پاسخ ارتعاشی اطالعات بسیار محدودی در مورد ترک ارائه می دهد در حالی که با تحریک همزمان مودهای باالتر، مؤلفه های هارمونیک متعددی به علت وجود ترک در پاسخ ارتعاشی ایجاد میشوند که حساسیت زیادی به ترک دارند و از تحلیل آنها اطالعات دقیقی در مورد موقعیت و عمق ترک حاصل می شود. | ||
| کلیدواژهها | ||
| تیر با ترک خستگی؛ ارتعاش چند مودی آزاد میرا؛ روش اغتشاشات؛ تحلیل فرکانسی | ||
| عنوان مقاله [English] | ||
| An Analytical Method for Damped Free Vibration Analysis of a Cracked Beam Considering the Coupled Multimode Equations | ||
| نویسندگان [English] | ||
| mousa rezaee1؛ vahid shaterian alghalandis2 | ||
| 2mechanical engineering department, university of tabriz | ||
| چکیده [English] | ||
| The multimodal free vibration of a beam with a breathing crack excited by arbitrary initial conditions is investigated. Taking the initial conditions to be arbitrary makes more than one mode of the beam to be excited simultaneously. By considering the bending moment at the crack position, a multi-harmonic function describing the instantaneous opening and closing of the crack is extracted. Since the modal stiffnesses of the beam are dependent on the crack parameters, the extracted crack breathing function will appear in the equations of motion and makes them to be coupled. These equations are solved using the perturbation method. Then, the free response of the beam is extracted under three cases of initial conditions: excitation of the first mode, simultaneous excitation of the first and second modes, and simultaneous excitation of the first three modes. The results show that by exciting the first mode solely, the harmonic components of the response offer very limited information about the crack. However, by exciting the first several modes simultaneously, many other harmonic components appears at the frequency response curves which are more sensitive to the crack and contain more comprehensive information about the crack parameters. | ||
| کلیدواژهها [English] | ||
| Beam with a fatigue crack, Multimode free damped vibration, Perturbation method, Frequency analysis | ||
| مراجع | ||
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