Vibration Analysis of FG Nanoplate Based on Third-Order Shear Deformation Theory (TSDT) and Nonlocal Elasticity

نویسندگان

  • M Raki Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran
  • M.M Najafizadeh Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran
  • P Yousefi Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran
چکیده مقاله:

In present study, the third-order shear deformation theory has been developed to investigate vibration analysis of FG Nano-plates based on Eringen nonlocal elasticity theory. The materials distribution regarding to the thickness of Nano-plate has been considered based on two different models of power function and exponential function. All equations governing on the vibration of FG Nano-plate have been derived from Hamilton’s principle. It has been also obtained the analytical solution for natural frequencies and corresponding mode shapes of simply supported FG Nano-plates. In addition, the general form of stiffness and mass matrix elements has been expressed based on this theory. The effect of different parameters such as power and exponential indexes of targeted function , nonlocal parameter of Nano-plate, aspect ratio and thickness to length ratio of Nano-plate on non-dimensional natural frequencies of free vibration responses have been investigated. The obtained analytical results show an excellent agreement with other available solutions of previous studies. The formulation and analytical results obtained from proposed method can be used as a benchmark for further studies to develop this area of research.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Vibration Analysis of a Rotating Nanoplate Using Nonlocal Elasticity Theory

The nanostructures under rotation have high promising future to be used in nano-machines, nano-motors and nano-turbines. They are also one of the topics of interests and it is new in designing of rotating nano-systems. In this paper, the scale-dependent vibration analysis of a nanoplate with consideration of the axial force due to the rotation has been investigated. The governing equation and b...

متن کامل

Vibration Analysis of FG Micro-Beam Based on the Third Order Shear Deformation and Modified Couple Stress Theories

In this paper, free vibration analysis and forced vibration analysis of FG doubly clamped micro-beams is studied based on the third order shear deformation and modified couple stress theories. The size dependent dynamic equilibrium equations and both the classical and non-classical boundary conditions are derived using a variational approach. It is assumed that all properties of the FG micro-be...

متن کامل

free vibration of functionally graded size dependent nanoplates based on second order shear deformation theory using nonlocal elasticity theory

in this article, an analytical solution is developed to study the free vibration analysis offunctionally graded rectangular nanoplates. the governing equations of motion are derived basedon second order shear deformation theory using nonlocal elasticity theory. it is assumed that thematerial properties of nanoplate vary through the thickness according to the power lawdistribution. our numerical...

متن کامل

Nonlocal Bending Analysis of Bilayer Annular/Circular Nano Plates Based on First Order Shear Deformation Theory

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) whic...

متن کامل

Forced vibration of piezoelectric nanowires based on nonlocal elasticity theory

In this paper, a numerical solution procedure is presented for the free and forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of Timoshenko beam theory. The influences of surface piezoelectricity, surface elasticity and residual surface stress are taken into consideration. Using Hamilton’s principle, t...

متن کامل

Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory

In this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. For this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. From the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...

متن کامل

منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


عنوان ژورنال

دوره 10  شماره 3

صفحات  464- 475

تاریخ انتشار 2018-09-30

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023