5/11/93

سعيد ضيايي راد، حميدرضا ميردامادي

مهندسي مكانيك

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3 چكيده در بسياري از كاربردها گرافن تكاليه يا چنداليه درون ماتريس پليمري به صورت كامپوزيت مورد استفاده قرار ميگيرد در اين پژوهش گرافن ايدهآل با شكل پيوندي ششضلعي بين اتمها واقع در ماتريس پليمري با شرايط مرزي مختلف شامل گيردار و ساده تحت بارگذاري فشاري خارجي دومحوره و بارگذاري حرارتي مورد بررسي قرار ميگيرد اين كامپوزيت به شكل تكاليه در نظر گرفته ميشود براي مدلسازي ابتدا جابهجاييها با استفاده از تئوري تغييرشكل برشي مرتبه سوم تخمين زده ميشوند و با استفاده از دو مدل وينكلر و پاسترناك ماتريس پليمري مدلسازي خواهد شد با استفاده از تئوري گراديان كرنش اينرسي معادالت تعادل ديناميكي بهدست آمده و با استفاده از روش مربعات ديفرانسيلي بهبود يافته معادالت حل ميشوند توزيع دما در سطح سازه با تابعيت خطي نسبت به طول و عرض صفحه و به شكل بار گسترده فرض ميشود فركانسهاي طبيعي و شكل مودهاي مربوطه كه وابسته به پارامترهاي سيستماند در دماهاي مختلف محاسبه ميگردد و اثر پارامترهايي مانند ضرايب وينكلر و پاسترناك پارامترهاي گراديان كرنش اينرسي و همچنين تعداد نقاط شبكهبندي مورد بررسي قرار ميگيرد از فركانسهاي طبيعي بسيار باالي بهدست آمده در اين پژوهش ميتوان سختي باالي سيستم را 3 نتيجه گرفت كلمات كليدي گرافن ارتعاشات نانوصفحه مربعات ديفرانسيلي بهبوديافته تغييرشكل برشي مرتبه سوم

05 Vibration Analysis of a Single Layer Graphene Sheet Embedded in an Elastic Medium Under Biaxial Compression Load Based on Strain Inertia Gradient Elasticity Theory Ayyub Ansari Rize e Ayyub ansari@me iut ac ir 1393 06 30 Department of Mechanical Engineering IsfahanUniversity of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Hassan Nahvi hnahvi@cc iut ac ir AbstractThe Stone Age the Bronze Age the Iron Age Every global epoch in the history of themankind is characterized by materials used in it In 2004 a new era in the material science wasopened the era of graphene or more generally of two dimensional materials Graphene is the one atom thin layer of sp2 bonded carbon atoms arranged in a honey comb lattice It possesses theunique physical properties graphene is the strongest and the most stretchable known material hasthe record thermal conductivity and the very high intrinsic mobility and is completelyimpermeable The charge carriers in graphene are the massless Dirac fermions and its uniqueelectronic structure leads to a number of interesting physical eff ects such as the minimal electricalconductivity anomalous quantum Hall effect Klein tunneling the universal optical conductivityand the strong nonlinear electromagnetic response Graphene offers and promises a lot of differentapplications including conductive ink terahertz transistors ultrafast photodetectors bendabletouch screens strain tensors and many other In many applications graphene single or multi layered is used within a polymer matrix incomposites form In this research an ideal graphene with hexagonal bonds between its atoms located in the polymer matrix under biaxial external pressure and thermal loadings is investigated The composite is single layer and different boundary conditions including clamped and simplysupported are considered For modeling of the problem firstly displacements are estimated using the third order sheardeformation theory and Winkler and Pasternak models are used to model polymer matrix Then dynamic equilibrium equations are obtained using the Strain Inertia Gradient theory and solvedusing Generalized Differential Quadrature GDQ method The temperature distribution is assumedto be linearly distributed in terms of the length and width of the structure Natural frequencies andcorresponding mode shapes which are depending on the system parameters are calculated atdifferent temperatures and the effect of parameters such as coefficients of Winkler and Pasternak Strain Inertia Gradient parameters and the number of lattice points are obtained The high hardnessof the system is resulted from very high natural frequencies obtained in this study Keywords Graphene Nanoplate vibration Generalized differential quadrature Thirdorder shear deformation

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سعيد ضيايي راد، حميدرضا ميردامادي