علوم و فناوری کامپوزیت

تحلیل فرکانسی تیر کامپوزیتی آلیاژ حافظه‌دار روی بستر الاستیک پاسترناک با استفاده از چهار نظریه مهندسی تیر

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد، دانشکده مهندسی هوافضا، دانشگاه فردوسی مشهد، مشهد، ایران

2 دانشیار، دانشکده مهندسی مکانیک، دانشگاه فردوسی مشهد، مشهد، ایران

چکیده

در چند دهه‌ی اخیر، تولید مواد هوشمند منجر به ایجاد سازه‌های برتر با خواص ممتاز شده است. از جمله‌ی این مواد می‌توان به آلیاژ‌های حافظه‌دار، که قابلیت بازیابی کرنش‌های پلاستیک بزرگ در اثر اعمال تنش یا حرارت را دارند، اشاره نمود. توسعه‌ی عملگر‌های آلیاژ حافظه‌دار به شکل‌های سیم و استنت در حوزه‌های مهندسی و سازه‌های هوشمند بسیار مورد توجه قرار گرفته است. در این راستا، مدل تحلیلی برای تیر کامپوزیتی با الیافی از جنس آلیاژ حافظه‌دار که روی بستر الاستیک پاسترناک قرار گرفته، ارائه شده است. تیر کامپوزیتی دارای تکیه‌گاه ساده در دو طرف بوده و الیاف حافظه‌دار با پیش-کرنش فشاری در لایه‌ی میانی تیر قرار گرفته‌اند. معادله‌های دیفرانسیل حاکم بر تیر‌های اولر-برنولی، رایلی، برشی و تیموشنکو با استفاده از اصل همیلتون استخراج شده‌اند. با اعمال حرارت، عملیات بازیابی کرنش، نیروی کششی در راستای طول تیر اعمال و این نیرو منجر به ایجاد نیروی فشاری در تکیه‌گاه‌ها می‌شود. نیروی ایجاد شده با استفاده از رابطه‌ی تغییر فاز مارتنزیتی مدل شده است. با بی‌بعد‌سازی معادله‌های دیفرانسیل حاکم، روابط تحلیلی برای ارزیابی پاسخ دقیق فرکانس طبیعی تیر ارائه شده است. اعتبار نتایج از طریق مقایسه‌ی موردی با تحلیل‌های مشابه مورد صحت‌سنجی قرار گرفته است. براساس تحلیل‌های انجام شده، تاثیر ضرایب بستر الاستیک پاسترناک، تعداد الیاف حافظه‌‌دار، نسبت ضخامت به طول تیر، حد کرنش قابل بازیابی و نسبت طول به پهنای تیر روی فرکانس طبیعی در دمای بالاتر از دمای پایان آستنیت براساس نظریه‌های مختلف مهندسی تیر تعیین و ارائه شده است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Frequency analysis of SMA composite beam resting on Pasternak elastic foundation using four engineering beam theories

نویسندگان [English]

  • Iman Rahimi Bafrani 1
  • Hamid Ekhteraei Toussi 2

1 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

چکیده [English]

In the last decades, the production of smart materials have led to modern structures with superior properties. Among these materials one may points to the Shape Memory Alloys (SMAs) which show the capability of retaining the large plastic strains when exposed to outer temperature or traction loadings. The developement of SMA acuators in the forms of wire and stent have attracted many attentions in the fields of engineering and smart structures. In this regard, an analytical model is represented for the composite beam with shape memory alloy wires resting on the Pasternak elastic foundation. The composite beam is simply-supported in both sides and pre-strained SMA wires are embedded in the middle of the cross section. The governing equations of Euler-Bernoulli, Rayleigh, Shear and Timoshenko beams are extracted using the Hamilton's principle. By heating the beam, strain recovery operation will produce a tensile force along the beam. This tensile force in turn will produce a compressive force against the beam supports. The resulted force is modeled by martensite transformation. By normalizing the governing equations, analytical relations are provided to evaluate the exact solution of natural frequency. The validity of results are established by comparing the typical solution with similar solution in the literature. Based on the analyses, the effects of Pasternak foundation coefficients, number of SMA wires, thickness to span ratio, recoverable strain limit and span to width ratio on the natural frequency in temperature above the austenite finish temperature are found and represented by using the engineering beam theories

کلیدواژه‌ها [English]

  • Frequency analysis
  • Composite beam
  • Shape memory alloy wires
  • Elastic foundation
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علوم و فناوری کامپوزیت
دوره 3، شماره 1
خرداد 1395
صفحه 73-84
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هم رسانی
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