Large Amplitude Vibration of Imperfect Shear Deformable Nano-Plates Using Non-local Theory
محورهای موضوعی : EngineeringS.K Jalali 1 , A Rastgoo 2 , I Eshraghi 3
1 - School of Mechanical Engineering, College of Engineering, University of Tehran
2 - School of Mechanical Engineering, College of Engineering, University of Tehran
3 - School of Mechanical Engineering, College of Engineering, University of Tehran
کلید واژه: Nonlinear vibration, Nonlocal theory, Shear Deformable Nano Plates, Geometric Imperfection,
چکیده مقاله :
In this study, based on nonlocal differential constitutive relations of Eringen, the first order shear deformation theory of plates (FSDT) is reformulated for vibration of nano-plates considering the initial geometric imperfection. The dynamic analog of the von Kármán nonlinear strain-displacement relations is used to derive equations of motion for the nano-plate. When dealing with nonlinearities, in the frame work of nonlocal theory, challenges are presented because of the coupling between nonlocal stress resultants and displacement terms. Governing equations are solved using differential quadrature method (DQM) and numerical results for free vibration of an imperfect single layered graphene sheet are presented.
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