Geometric/microstructural imperfection sensitivity in the vibration characteristics of geometrically non-uniform functionally graded plates with mixed boundary conditions

Abstract

In the present article, the vibration response of geometrically imperfect functionally graded material (FGM) plates with geometric discontinuities and microstructural defects have been investigated. The structural kinematics used in the present study is based on logarithmic shear-strain function. A refined generalized porosity model has been developed to encompass even and uneven types of porosity models available in the literature. The geometric discontinuities have been assimilated in terms of a circular cutout of different sizes at the center of the plate. To incorporate the geometric imperfection, a generic function has been used. A C⁰ continuous iso-parametric finite element formulation has been used to attain the results whereas the accuracy of the present solution has been confirmed by comparing the results with the available literature. The analysis reveals that after a specific cutout radius, the FGM plates exhibit the nonlinear vibration characteristics. It has been observed that the influence of boundary conditions, cutout dimensions, geometric imperfections, and porosity inclusions on frequency parameters are significant. Most of the results presented in this paper are novel and may be treated as benchmark results for future reference.

Keywords:

• Functionally graded material
• geometric imperfection
• porosity inclusions
• cutout size
• unconventional boundary constraints