IJE TRANSACTIONS A: Basics Vol. 31, No. 7 (July 2018) 1095-1102    Article in Press

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E. Allahyari and M. Asgari
( Received: December 05, 2017 – Accepted in Revised Form: March 09, 2018 )

Abstract    Free vibration characteristics of polymer composite plates reinforced by graphene nanosheets employing the Eringen nonlocal elasticity theory were investigated. Theoretical formulations are derived based on Hamilton’s principle implementing linear orthotropic constitutive equations of lamina while the behavior of nanostructure points affected by all other nonlocal points is also taken into account. For obtaining the mechanical properties, a new modified Halpin–Tsai model is employed. Governing equations are solved by developing an efficient analytical solution. The accuracy of the presented method is examined, by comparing the results with literature in which a good agreement is observed. Effects of different boundary conditions, volume fraction, graphene sheets orientation angle and Eringen nonlocal parameter on frequency of nanocomposite are analyzed. Effects of the presence of vacancy defects in the nanosheet on the behavior of reinforced composites were also studied. The results illustrate that by increasing the nonlocal parameter the natural frequency showed a decreasing trend while by increasing the graphene sheet’s volume fraction, natural frequencies significantly increased. It could be concluded that the orientation angle variations in graphene sheets, did not play an important role on the natural frequency of nanocomposite as well as degradation of properties resulted in from vacancy defects.


Keywords    Nanocomposite; Graphene Sheets; Free Vibration; Eringen Nonlocal Theory; Vacancy Defect; Analytical Solution


چکیده    ارتعاش آزاد ورق­های کامپوزیت پلیمری که با نانوورق­های گرافن تجهیز شده­اند با استفاده از تئوری الاستیسیته غیرمحلی ارینگن مورد بررسی قرار گرفته­اند. روابط تئوری با بکارگیری اصل همیلتون و معادلات خطی و ساختاری چندلایه ارتوتروپیک که نیز در آن رفتار نقاطی از نانوسازه تحت تاثیر دیگر نقاط غیرمحلی می­باشد استخراج شده است. به­منظور به دست آوردن خواص مکانیکی، فرم ارتقاء یافته هالفین-تسای بکار گرفته شده است. معادلات پایه با استفاده از یک روش تحلیلی به دست آمده­اند. دقت روش ارائه شده با مقایسه نتایج آن با دیگر مقالات بررسی شده است که تطابق خوبی مشاهده شده است. اثرات شرایط مرزی مختلف، درصد حجمی، زاویه جهت­گیری ورق­های گرافن و پارامتر غیرمحلی ارینگن بر روی فرکانس نانوکامپوزیت مورد بررسی قرار گرفته­اند. اثرات وجود عیوب شبکه در نانوورق بر روی رفتار کامپوزیت­های تقویت شده نیز مورد بررسی قرار گرفته­اند. نتایج نشان می­دهد که با افزایش پارامتر غیرمحلی فرکانس طبیعی تمایل به نشان دادن رفتاری نزولی دارد درحالیکه با افزایش درصد حجمی نانو گرافن، فرکانس­های طبیعی به طور محسوسی افزایش می­یابند. می­توان نتیجه گرفت که زوایای مختلف جهت­گیری ورق­های گرافن همچنین افت خواص ایجاد شده به واسطه عیوب شبکه، نقش مهمی در فرکانس طبیعی نانوکامپوزیت نخواهند داشت.


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