نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار، دانشکده مهندسی مکانیک، دانشگاه سمنان، سمنان، ایران

2 دانشجوی کارشناسی ارشد، دانشکده مهندسی مکانیک، دانشگاه سمنان، سمنان، ایران

10.22068/jstc.2018.81209.1418

چکیده

در این مقاله به بررسی ارتعاشات میکروپنل کامپوزیتی پلیمری هوشمند پلی وینیلیدن فلوراید تقویت شده با نانولوله نیترید بور تحت تاثیر میدان الکتریکی واقع بر بستر الاستیک با استفاده از تئوری برشی مرتبه اول پرداخته شده است. نحوه توزیع نانولوله‌ها در بستر پلیمری به صورت یکنواخت فرض می‌شود. برای مدل‌سازی بستر الاستیک از فنرهای وینکلر و لایه‌ی برشی پاسترناک و برای بررسی اثرات اندازه از تئوری مرتبه بالای گرادیان کرنش اصلاح شده استفاده شده است. در ابتدا با استفاده از روش مدل-سازی میکرومکانیک، معادلات ساختاری نانوکامپوزیت برای یک المان حجمی نمونه استخراج شده و سپس روابط تنش- کرنش بر حسب ترم‌های مکانیکی و الکتریکی به دست آمده است. همچنین معادلات حرکت به کمک اصل همیلتون به دست آمده و در نهایت با استفاده از روش حساب تغییرات و با استخراج ماتریس‌های جرم و سختی، فرکانس طبیعی میکروپنل به دست می‌آید. نتایج به دست آمده در این مقاله نشان می‌دهد که با افزایش نسبت ابعادی و کاهش درصد حجمی نانولوله‌ها، سختی پنل کاهش یافته و فرکانس طبیعی نیز کاهش می‌یابد. در ادامه پارامترهای مختلفی از قبیل سفتی بستر الاستیک، میزان تاثیر میدان الکتریکی، مودهای مختلف ارتعاشی، نسبت ابعادی و سایر عوامل بررسی شده است. همچنین مقایسه ای بین تئوری های کلاسیک، تنش کوپل اصلاح شده و گرادیان کرنش اصلاح شده انجام شده است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Vibration analysis of boron nitride-reinforced nanocomposites embedded in elastic medium considering surface and electric field effects by using higher-order modified strain gradient theory

نویسندگان [English]

  • Ahmad Ghasemi-Ghalebahman 1
  • Elham Cheloeian 2

1 Department of Mechanical Engineering, Semnan University, Semnan, Iran

2 Department of Mechanical Engineering, Semnan University, Semnan, Iran

چکیده [English]

This paper investigates free vibration of a smart sandwich composite polymeric micro-panel blend of polyvinylidene fluoride reinforced with boron nitride nanotubes under an electric field resting on an elastic substrate using first order shear deformation theory. The distribution of nanotubes in the polymeric matrix is assumed uniformly. The Winkler springs and Pasternak shear layer are used for modeling the elastomeric substrate and the higher-order modified strain gradient theory is implemented to investigate the effects of size. First, using the microstructural modeling technique, the constitutive equations of the nanocomposite are extracted for a representative volume element, and then the stress-strain relations are obtained in terms of mechanical and electrical terms. Also, the equations of motion are derived using the Hamilton principle, and finally using the method of variational calculus and extracting the mass and stiffness matrices, the natural frequency of the micro-panel is obtained. The results of this paper show that by increasing the aspect ratio and reducing the volume fraction of nanotubes, the panel's hardness decreases and the natural frequency decreases. Further, various parameters such as the stiffness of elastic medium, the effect of electric field, different modes, aspect ratio and other factors are investigated. A comparison is also made between the classical, modified coupled stress, and higher-order modified strain gradient theories.

کلیدواژه‌ها [English]

  • Free vibration
  • Smart polymeric nanocomposite
  • Higher-order modified strain gradient theory
  • Boron nitride nanotube
  • Electric field
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