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اصلاح رفتار ارتعاشی آزاد در تیر تیموشنکوی دوار دارای ترک با استفاده از اتصالات پیزوالکتریک و به کارگیری روش تبدیل دیفرانسیل | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 8، دوره 51، شماره 1، فروردین و اردیبهشت 1398، صفحه 97-108 اصل مقاله (1.08 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2017.12541.5360 | ||
| نویسندگان | ||
| محمد مهدی نادری؛ علیرضا آریایی* | ||
| دانشکده فنی و مهندسی، گروه مهندسی مکانیک، دانشگاه اصفهان، اصفهان، ایران | ||
| چکیده | ||
| در این مقاله یک روش تحلیلی جهت استفاده از اتصالات پیزوالکتریک برای اصلاح رفتار ارتعاشی آزاد در یک تیر دورانی ترک دار ارائه می‌شود. معادلات تیر بر مبنای تئوری تیموشنکو و با در نظر گرفتن اثر تغییر شکل برشی و اینرسی دورانی به دست می‌آیند. معیار مورد استفاده جهت اصلاح ترک افزایش فرکانس اول تیر دارای ترک و منطبق کردن آن بر فرکانس تیر سالم است. بدین منظور یک ولتاژ خارجی به وصله پیزوالکتریک متصل به تیر اعمال می‌شود که از میزان نقش ترک بر تغییر ویژگی‌های ارتعاشی تیر می‌کاهد. ابتدا معادلات دیفرانسیلی کوپل تیر تیموشنکو با روش مودهای فرضی از هم جدا می‌شوند. سپس تیر تر کدار به صورت بخش‌هایی بدون ترک مدل می‌شود که در محل ترک با دو فنر خطی، یکی کششی و دیگری پیچشی، به هم متصل شده‌اند. در نهایت با استفاده از روش نیمه تحلیلی تبدیل دیفرانسیل، فرکانس های طبیعی و شکل مودهای سیستم به دست می‌آیند. با انجام یک شبیه‌سازی عددی، تأثیر پارامترهای مختلف بر ضریب اصلاح ترک مطالعه می‌گردد. اعتبار روش ارائه شده با مقایسه نتایج آن با مقادیر موجود در سایر مقالات مورد بررسی قرار می‌گیرد که تطابق قابل قبولی بین نتایج مشاهده می‌شود. | ||
| کلیدواژه‌ها | ||
| اصلاح فعال؛ عملگر پیزوالکتریک؛ تیر تیموشنکوی ترک‌دار؛ تیر دوار؛ روش تبدیل دیفرانسیل | ||
| عنوان مقاله [English] | ||
| Repair of Free Vibration Behavior of a Cracked Rotating Timoshenko Beam Using a Piezoelectric Patch and Applying Differential Transform Method | ||
| نویسندگان [English] | ||
| M. Naderi؛ A. Ariaei | ||
| Department of Mechanical Engineering, University of Isfahan, Isfahan, Iran | ||
| چکیده [English] | ||
| This paper presents an analytical method for the application of piezoelectric patches to repair a rotating cracked beam. The beam equations of motion are obtained based on the Timoshenko beam theory including the effects of shear deformation and rotary inertia. The criterion applied for the repair is to modify the first natural frequency of the cracked beam towards that of the healthy beam applying a piezoelectric patch. Due to this, an external voltage is applied to actuate a piezoelectric patch bonded on the beam that decreases the effect of the crack on the vibration characteristics of the beam. First, the coupled equations of motion are discretized by applying the assumed modes method. Then, the cracked beam is modeled as numbers of healthy segments connected by two linear springs at the crack locations (one, extensional and the other, rotational). The compatibility requirements on the crack section and on the ends of the piezoelectric patch are considered to obtain the relationships between any two spans. Finally, applying the semi-analytical differential transform method, the natural frequencies and mode shapes of the system can be calculated. Numerical simulations are performed to assess the effects of different conditions on the repair moment coefficient. The presented model is validated by comparing the results with those available in the literature where, the natural frequencies are in a reasonably good agreement with the reported results. | ||
| کلیدواژه‌ها [English] | ||
| Active repair, Piezoelectric actuator, Cracked Timoshenko beam, Rotating beam, Differential transform method | ||
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سایر فایل های مرتبط با مقاله
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| مراجع | ||
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