Nonlinear vibration of a nanoplate embedded on a Pasternak-type foundation using nonlocal continuum theory

Nonlinear vibration of a nanoplate embedded on a Pasternak-type foundation using nonlocal continuum theory

BY: Payam Soltani, V. Kamali , O. Pashaei Narenjbon,  A. Farshidianfar 

Abstract:

Nonlocal plate continuum model is utilized to investigate the nonlinear vibration behaviour of a singlelayer

nanoplate. The isotropic nanoplate is assumed to be embedded on a Pasternak-type elastic foundation with the

simply supported boundary conditions. The Hamilton’s principle is applied to derive the governing equation of motion,

and the nonlinear frequency is obtained analytically using perturbation approach. The results indicate that the nonlinear

frequency is significantly dependent on the maximum amplitude. Furthermore, the nonlinear frequency increases with

an increase in the nonlocal parameter, which means that the nonlinear frequency based on the local plate theory are

underestimated. Furthermore, for arbitrary maximum amplitude, the variations of the nonlinear frequency against the

nonlocal parameter, aspect ratio, Pasternak-type foundation constants, and size effects of the nanoplate are investigated.

The present communication may be useful for designing nanomechanical devices and nano-electromechanical systems. 

http://icns4.nanosharif.ir/proceedings/files/proceedings/MOD060.pdf