بررسی گسترش موج در نانوصفحه مدرج تابعی تحت بار حرارتی غیرخطی روی بستر الاستیک براساس نظریه پالایش یافته چهار متغییره

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده فنی و مهندسی، دانشگاه بین المللی امام خمینی (ره)، قزوین، ایران

چکیده

در این مقاله از یک روش حل تحلیلی به منظور مطالعه اثرات بارگذاری حرارتی روی یک نانوصفحه مدرج تابعی قرار گرفته روی بستر الاستیک با استفاده از یک نظریه چهار متغیره پالایش شده استفاده شده است. بارگذاری حرارتی مورد استفاده از نوع رسانش گرمایی می‌باشد که در این پژوهش از تغییرات غیرخطی دما استفاده شده است. با به کارگیری روابط انتقال حرارت جابه جایی روابط توزیع دمای غیرخطی در راستای ضخامت صفحه به دست آمده اند. خواص فیزیکی وابسته به دمای نانوصفحه با استفاده از مدل موری-تاناکا درجه‌بندی شده اند. برای در نظر گرفتن اثرات مقیاس کوچک از نظریه غیرمحلی ارینگن استفاده شده است. معادلات حاکم با به کارگیری اصل همیلتون به دست آمده‌اند. بسامدهای به دست آمده با مقایسه با تحقیقات اخیر صح تسنجی شده اند. علاوه بر این، اثرات پارامترهای گوناگون مثل توزیع دما، ضرایب بستر الاستیک، پارامتر غیرمحلی و شاخص گرادیان بر روی گسترش موج نانوصفحه وابسته به اندازه مدرج تابعی مورد بررسی قرار گرفته است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Wave Propagation in Embedded Temperature-dependent Functionally Graded Nano-plates Subjected to Nonlinear Thermal Loading According to a Nonlocal Four-variable Plate Theory

نویسندگان [English]

  • F. Ebrahimi
  • A. Dabbagh
Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran.
چکیده [English]

In this article, an analytical approach is used to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded nano-plate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nano-plate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by means of Hamilton’s principle. Obtained frequencies are validated with those of previously published works. Moreover, effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter and gradient index on the wave propagation response of size-dependent functionally graded nano-plates have been investigated.

کلیدواژه‌ها [English]

  • Nonlocal wave propagation
  • Four-variable plate theory
  • Inhomogeneous nano-plate
  • Mori-Tanaka model
  • Thermal effects
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