Application of the G/XFEM, quasi-3D theory, and the nonlocal elasticity in the vibration analysis of thick functionally graded nano-plates

Resumo

In this study, the problem of free vibrations in functionally graded moderately thick nanoplates is
addressed. The numerical models are obtained employing the quasi-3D plate theory and the approximation spaces
are obtained according to the G/XFEM with PU's with regularity

, = 1,2. The choice to use the cited
approximation spaces is related to their regularity, which is extremely relevant in non-local dynamic elastic
problems. In this sense, the use of approximation spaces obtained with

FEM-Lagrange produces significant
differences in the nanoscale result which does not occur in classical or local elasticity. In the case studies, the
following effects on the first resonance frequency are analyzed: increase in the nanoplate size, distribution of the
biphasic material, and increment of the nanoscale parameter. As a complementary result, the effect of the regularity
of the approximation spaces in the verification of the stiffness softening phenomenon is analyzed. The normalized
frequencies resulting from those obtained with high order FEM-Lagrange, a semi-analytic solution, and the
Hermitian elements (H-FEM)

, = 1,2.