تحلیل الکترومکانیک استوانه چرخان ساخته شده از مواد پیزوالکتریک مدرج تابعی به کمک نظریه تغییر شکل برشی مرتبه بالا: حسگر و عملگر

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی مکانیک، دانشکده فنی و مهندسی، دانشگاه یاسوج، یاسوج، ایران

10.22060/mej.2017.11983.5236

چکیده

در این مقاله بر مبنای نظریه تغییرشکل برشی مرتبه بالا، معادلات الکتروالاستیک حاکم بر استوانه‌های جدار ضخیم متقارن محوری ساخته شده از مواد ناهمگن مدرج تابعی در حالت کلّی استخراج شده است. جابه جایی‌ها، تن شها و پتانسیل الکتریکی برای استوانه با دو سر بسته مقید، به صورت تحلیلی به دست آمده است. این راهکار منجر به تعریف فرمولاسیون جدید برای تحلیل پوسته‌های جدار ضخیم بر پایه نظریه تغییرشکل برشی شده است. معادلات تعادل مکانیکی به روش انرژی به دست آمد و برای یافتن معادلات تعادل الکتریکی از معادلات ماکسول و گاوس استفاده شد. حل معادلات حاکم در حالت عمومی )مستقل از مرتبه نظریه تغییرشکل برشی( به صورت کوپل مکانیکی-الکتریکی و با استفاده از روش بردارهای ویژه ارائه شد. در این بررسی تمامی خواص الکترومکانیک در راستای شعاعی به صورت تابع توانی فرض شده است. به منظور بررسی صحت نتایج، جابه جایی شعاعی، پتانسیل الکتریکی و تنش شعاعی استوانه جدار ضخیم همگن با نظریه‌ی الاستیسیته مستوی مقایسه و شباهت ها نشان داده شده است. به منظور بررسی تأثیر افزایش مرتبه نظریه‌ی تغییرشکل برشی بر مقادیر جابه‌جایی‌ها، تنش‌ها و پتانسیل الکتریکی، مقایسه‌ای بین نتایج حاصل از نظریه‌ی تغییرشکل برشی مرتبه اول و سوم صورت گرفته است. نتایج نشان می‌دهد که استفاده از تقریب مرتبه بالا برای تحلیل الکتروالاستیک پوسته‌های استوانه‌ای ساخته شده از مواد پیزوالکتریک مدرج تابعی ضروری است. در انتها با بهره‌گیری از روش ارائه شده، تأثیر بارگذاری‌های الکتریکی و مکانیکی بر رفتار تنش‌ها، جابه جایی‌ها و توزیع پتانسیل الکتریکی سیلندر بررسی شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Electro-mechanical Analysis of Rotating Cylinder Made of Functionally Graded Piezoelectric Materials: Sensor and Actuator

نویسندگان [English]

  • M. Jabbari
  • Mohammad Zamani Nejad
Mechanical Engineering Department, Yasouj University, Yasouj, Iran
چکیده [English]

In this paper, based higher shear deformation theory, electro-elastic equation of functionally graded material axisymmetric thick-walled cylinders in general form is presented. The displacements, stresses and electrical potential in clamped-clamped cylindrical shells analytically are calculated. The presented approach leads to the definition of new formulation to study thick shells based on shear deformation theory. The mechanical equilibrium equation obtained by energy method and for finding electrical equilibrium equation used Maxwell and Gauss equations. The governing equation solved in general form (independent of the order of shear deformation theory) by the coupled electro-mechanical using eigen vectors In this study, all mechanical and electrical piezoelectric material properties, were considered to follow an identical power law in the radial direction. The results obtained in the present paper have been compared with findings of plane elasticity theory. For investigating the effect of higher order approximations on displacements and stresses and electrical potential, a comparison between the results of first and third-order shear deformation theory have been studied. The numerical results show that the higher-order approximations must be applied in electro-elastic analysis of cylindrical shells made of functionally graded piezoelectric material. Finally, some numerical results are presented to study the effects of mechanical and electrical loading on the stresses, displacements and electrical potential of the cylinder.

کلیدواژه‌ها [English]

  • Electromechanical analysis
  • rotating cylindrical shell
  • Shear deformation theory
  • Functionally graded material
  • Piezoelectric material
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