تحلیل ارتعاشات آزاد ورق‌های تاخورده مورب مرکب تقویت‌شده با نانولوله‌های کربنی به صورت مدرج تابعی با استفاده از رویکرد آیزوژئومتریک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک و هوافضا، دانشگاه صنعتی شیراز، شیراز، ایران

2 هیات علمی-دانشگاه صنعتی شیراز

چکیده

در این پژوهش، یک رویکرد بر مبنای روش آیزوژئومتریک جهت مطالعه رفتار ارتعاشات آزاد ورق‌های تاخورده مورب مرکب تقویت‌شده با نانولوله‌های کربنی به صورت مدرج تابعی توسعه داده شده است. در این روش از توابع پایه بی‌اسپیلاین کسری غیریکنواخت به منظور تقریب هندسه و همچنین میدان تغییرمکان استفاده می‌گردد. این ورق‌ها به وسیله نانولوله‌های کربنی تک‌جداره تقویت شده‌اند که فرض می‌شود توزیع این نانولوله‌ها در امتداد ضخامت ورق به صورت مدرج تابعی با الگوهای مختلف است. خواص مکانیکی موثر ورق‌های تاخورده مورب مرکب به کمک قاعده مخلوط‌های اصلاح‌شده محاسبه گردیده است. مدلسازی ورق تاخورده مورب با دو وصله نربز انجام گرفته است که از نقاط قوت پژوهش می‌باشد. معادلات حاکم بر هر وصله بر مبنای تئوری ورق کلاسیک استخراج گردیده و سپس با استفاده از توابع پایه نربز گسسته‌سازی شده‌اند. فرم نهایی معادلات گسسته، پس از انتقال ماتریس‌های المانی هر وصله با استفاده از یک تبدیل مختصاتی مناسب و سپس اعمال شرایط پیوستگی در مرز بین وصله‌ها به کمک روش نوار خمشی ایجاد شده است. سپس، چندین مثال عددی برای اثبات دقت و اعتبار فرمول‌بندی پیشنهادی تهیه شده است. نتایج نشان می‌دهد که رویکرد حاضر می‌تواند با دقت زیادی فرکانس‌های طبیعی ورق تاخورده مورب را با هزینه محاسباتی کم پیش‌بینی نماید. در نهایت یک مجموعه نتایج جدید برای پارامترهای مختلف هندسی و مادی ورق تاخورده مورب ارائه گردیده است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Free vibration analysis of functionally graded carbon nanotubes reinforced composite skew folded plates using the isogeometric approach

نویسندگان [English]

  • Hassan Mohammadi 1
  • Ali Reza Setoodeh 2
1 Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, Iran
2 Associate Professor/Shiraz University of Technology
چکیده [English]

In this research, an approach based on the isogeometric method is developed to study the free vibration behavior of functionally graded carbon nanotubes reinforced composite skew folded plates. In this method, non-uniform rational B-splines basis functions are used for approximation of the geometry as well as the displacement field. The plates are reinforced by single-walled carbon nanotubes which are assumed to be graded through the thickness direction with different distribution patterns. The effective mechanical properties of composite skew folded plates are captured by the modified rule of mixtures approach. Modeling of the skew folded plate is accomplished by two non-uniform rational B-splines patches which is one of the strengths of the research. The equations of motion of each patch are derived based on classical plate theory and then are discretized using non-uniform rational B-splines basis functions. The final form of the discretized equations is generated after the transformation of the element matrices of each patch and then applying the continuity conditions along the boundary of the patches with the aid of the bending strip method. Afterward, several numerical examples are provided to prove the accuracy and reliability of the proposed formulation. The results exhibit that the present approach can precisely predict the natural frequencies of skew folded plates with a low computational cost. Eventually, a set of new results are presented for different geometrical and material parameters of the skew folded plate.
 

کلیدواژه‌ها [English]

  • Isogeometric analysis
  • Bending strip method
  • Skew plates
  • Folded plates
  • Carbon nanotubes

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نشریه مهندسی مکانیک امیرکبیر
دوره 53، شماره 4
تیر 1400
صفحه 2239-2260

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