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Steel and Composite Structures
  Volume 32, Number 2, July25 2019 , pages 281-292
DOI: https://doi.org/10.12989/scs.2019.32.2.281
 


The application of nonlocal elasticity to determine vibrational behavior of FG nanoplates
A.M. Fattahi, Babak Safaei and E. Moaddab

 
Abstract
    Nonlocal elasticity and Reddy plant theory are used to study the vibration response of functionally graded (FG) nanoplates resting on two parameters elastic medium called Pasternak foundation. Nonlocal higher order theory accounts for the effects of both scale and the effect of transverse shear deformation, which becomes significant where stocky and short nanoplates are concerned. It is assumed that the properties of FG nanoplate follow a power law through the thickness. In addition, Poisson\'s ratio is assumed to be constant in this model. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of nanoplate with surrounding elastic medium. Using Hamilton\'s principle, size-dependent governing differential equations of motion and corresponding boundary conditions are derived. A differential quadrature approach is being utilized to discretize the model and obtain numerical solutions for various boundary conditions. The model is validated by comparing the results with other published results.
 
Key Words
    vibration; functionally graded nanoplate; nonlocal theory; elastic foundation
 
Address
(1) A.M. Fattahi:
Department of Mechanical Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran;
(2) Babak Safaei:
Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China;
(3) E. Moaddab:
Seraj Institute of Higher Education, Tabriz, Iran.
 

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