تحلیل دوبعدی الکتروالاستیک استوانه‌های جدار ضخیم پیزوالکتریک با استفاده از نظریه‌های تغییر شکل برشی و پتانسیل الکتریکی مرتبه یک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه جامدات، دانشکده مهندسی مکانیک و مکاترونیک، دانشگاه صنعتی شاهرود، شاهرود، ایران

2 صنعتی شاهرود

چکیده

امروزه، عملگرها و حسگرها، جایگاه ویژه‌ای در جهان علم و صنعت دارند. بنابراین تحلیل الکتروالاستیک مواد پیزوالکتریک از موضوعات مورد توجه‌ پژوهشگران بوده تا بتوانند درک صحیحی از رفتار سازه‌‌ها بیابند و با بهینه‌سازی آن‌ها، گام مؤثری در طراحی و ساخت سازه‌ها بردارند. در پژوهش حاضر با استفاده از روش انرژی، نظریه‌ تغییر شکل برشی مرتبه‌ یک و نظریه پتانسیل الکتریکی مرتبه یک، معادلات حاکم استوانه‌ها‌ی جدار ضخیم پیزوالکتریک که تحت بارگذاری الکتریکی و مکانیکی در لایه‌های داخلی و خارجی استوانه و دارای شرایط مرزی مختلف در دو سر استوانه، استخراج شده است. سپس یک حلّ تحلیلی و ریاضی برای دستگاه معادلات حاکم بر پوسته استوانه‌ای ارائه می‌شود و با استفاده از این حل، نتایج مربوط به رفتار الکترومکانیکی استوانه برای شرایط مرزی مختلف الکتریکی و مکانیکی استخراج شده و با نتایج عددی حاصل از روش اجزای محدود مقایسه و بررسی می‌شوند. حل تحلیلی ارائه شده در این پژوهش، زیرمجموعه حل‌های سری‌گونه نیست و نیاز به بررسی همگرایی پاسخ ندارد. هم‌چنین حل ارائه ‌شده، از حجم محاسباتی کم‌تری نسبت به حل‌های سری‌گونه برخوردار است. نتایج به‌دست آمده از دو روش تحلیلی و عددی، دارای تطابق خوبی بوده و نشان می‌دهند که حل تحلیلی ارائه شده با دقّت مطلوب، قابل استفاده می‌باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

2-Dimensional Electroelastic Analysis of Piezoelectric Cylinders Using First-Order Shear Deformation and First-Order Electric Potential Theories

نویسندگان [English]

  • Mohammad Parhizkar Yaghoobi 1
  • Mahdi Ghannad 2
1 Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran
چکیده [English]

Today, sensors and actuators have a special place in the science and industry world. Therefore, the electromechanical analysis of piezoelectric materials is one of the topics of interest for researchers. To that effect, besides understanding the behavior of piezoelectric structures by optimizing this behavior, they could facilitate designing and manufacturing structures. In this study, using the first-order shear deformation theory and the first-order electrical potential theory and applying the energy method, the governing equations are extracted for thick piezoelectric cylinders subjected to mechanical and electrical loading at their internal and external surfaces under various boundary conditions in two cylinder heads. Then an analytical solution is presented for the governing equations. Using this solution, the results of the electromechanical behavior of the cylinders under different boundary conditions in two cylinder heads are estimated and evaluated. Then these results are compared with the finite element method’s results. The analytical solution is not a series solution, and therefore there would be no need to investigate the convergence. Furthermore, it is of less computational volume. The results obtained from the analytical method and the finite element method have a good agreement, showing that the presented analytical solution can be used with higher accuracy.

کلیدواژه‌ها [English]

  • Thick cylinder
  • Piezoelectric
  • Shear deformation theory
  • First-Order Electrical Potential theory
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