Modelling vibrations of a moderate amplitude in piezoelectric nanoplates using nonlocal elasticity and G/XFEM

Resumo

In this paper, we address the problem of free and unforced vibration of nanoplates immersed in a transverse electric field using the theory of non-local elasticity. The numerical model was obtained using the first-order plate kinematic theory, which included the shear deformation (FSDT) and the approximation spaces in accordance with the homogeneous “p” version of the G/XFEM method with regularity C k, k = 2, 4. The scale effect is approached using the non-local elasticity theory, and moderate amplitude waves are taken into consideration using the von Karmann geometric non-linearity. In this study an electric stationary field is obtained from a potential function that satisfies Maxwell’s law for moving current and the electric potential boundary conditions on the free surface
of the plate. Investigations on the estimation of the first nonlinear frequency, as well as the stiffness-softening and stiffness-hardening phenomena, are carried out for a simply supported nanoplate. The findings for the proposed numerical models are contrasted with those attained using Lagrange C 0 finite elements, a semi-analytical solution attained using Navier biharmonic modes, and results acquired using the Generalized Differential Quadrature Method (GDQM) from published results. The GFEM approximation space demonstrated its ability to describe all features of the problem at hand.