تحلیل ارتعاشات آزاد و اجباری مواد پیزوالکتریک مبتنی بر روش نیمه‌تحلیلی اجزاء محدود با مرز مقیاس شده

نوع مقاله : مقاله پژوهشی

نویسندگان

1 صنعتی شاهرود-مهندسی مکانیک

2 پژوهشکده فناوری نو، دانشگاه صنعتی امیرکبیر

چکیده

امروزه استفاده از مواد پیزوالکتریک به‌عنوان گونه‌ای از مواد هوشمند در صنایع مختلف توسعه چشمگیری داشته است. مدل‌سازی دقیق رفتار این مواد، نقش مهمی در درک مکانیزم عملکردی و همچنین گسترش روش‌های جدید مبتنی بر رفتار وابسته الکتریکی-مکانیکی آن‌ها ایفا می‌کند. این در حالی است که هزینه بالای محاسباتی روش‌های عددی موجود برای شبیه‌سازی رفتار ارتعاشی مواد پیزوالکتریک، به‌خصوص در فرکانس‌های بالا، از چالش‌های جدی این حوزه محسوب می‌شود. هدف از این پژوهش استفاده از یک روش نیمه‌تحلیلی نوین موسوم به روش اجزاء محدود با مرز مقیاس‌شده به‌منظور تحلیل ارتعاشات آزاد و اجباری وصله‌های پیزوالکتریک است. ترکیب اصول حاکم بر دو روش عددی اجزاء محدود و اجزاء مرزی در روش حاضر، امکان تحلیل هرگونه معادله مشتق جزئی را به‌صورت نیمه‌تحلیلی با هزینه محاسباتی بسیار پایین‌تر نسبت به روش اجزا محدود را فراهم می‌کند. به‌منظور ارزیابی دقت این روش در مدل‌سازی مسائل مختلف مانند رفتار ماده پیزوالکتریک در مسائل پایش سلامت و همچنین مکانیک شکست، 4 مسئله موردی شامل ارتعاشات آزاد و اجباری وصله پیزوالکتریک، وصله پیزوالکتریک متصل به سازه آلومینیومی، وصله پیزوالکتریک سوراخ‌دار و وصله پیزوالکتریک ترک‌خورده مورد تحلیل قرار گرفت. مقایسه نرخ همگرایی روش‌های اجزاء محدود با مرز مقیاس شده و اجزاء محدود نشان از دستیابی به نتایج دقیق به ازای تعداد درجات آزادی بسیار کمتر در روش اول دارد. به‌علاوه، تطابق مناسب نتایج حاصل از این دو روش، نشان از قابلیت روش اجزاء محدود با مرز مقیاس‌شده در مدل‌سازی انواع مسائل با هزینه محاسباتی بسیار پایین دارد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Free and Forced Vibration Analysis of Piezoelectric Patches Based on Semi-Analytic Method of Scaled Boundary Finite Element Method

نویسندگان [English]

  • Naserodin Sepehry 1
  • Mohammad Ehsani 2
  • Mahnaz Shamshirsaz 2
1 صنعتی شاهرود-مهندسی مکانیک
2 New Technologies Research Center (NTRC), Amirkabir University of Technology
چکیده [English]

Development of a precise mathematical model of piezoelectric patches plays an important role in comprehending their operational mechanisms as well as developing new techniques based on their coupled electro-mechanical behavior. While, high computational cost of available numerical methods which are able to simulate vibrational behavior of piezoelectric patches, especially at high frequencies, is considered as a serious challenge in this area. The purpose of this study is to use a novel semi[1]analytical method, called Scaled Boundary Finite Element Method, to analyze free and forced vibration of piezoelectric patches. In order to evaluate the accuracy of this method in modeling of different problems occurred in structural health monitoring and fracture mechanics, the free and forced vibration of a piezoelectric patch, a piezoelectric patch attached to an aluminum structure, a piezoelectric patch with a circular hole and a cracked piezoelectric patch was analyzed as four case studies. Comparison of convergence rate of scaled boundary finite element method and finite element method indicates that the former provides exact results with much less degrees of freedom. In addition, proper matching of results demonstrates the capability of scaled boundary finite element method to model a variety of problems accurately at a very low computational cost.

کلیدواژه‌ها [English]

  • Scaled boundary finite element method
  • Electro-mechanical coupled field
  • Vibration
  • Piezoelectric patch
  • Finite element method
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