Isogeometric small-scale-dependent nonlinear oscillations of quasi-3D FG inhomogeneous arbitrary-shaped microplates with variable thickness

Abstract

The current investigation deals with proposing a numerical analysis for the geometrically nonlinear large-amplitude vibrations of arbitrary-shaped microplates having variable thickness with various patterns in the presence of couple stress type of microstructural size dependency. To accomplish this purpose, the isogeometric analysis (IGA) is employed to achieve exact geometrical description as well as higher-order efficient smoothness with no meshing difficulty. On the other hand, the modified couple stress continuum mechanics is applied to a refined quasi-3D plate model having the capability to take the thickness stretching into consideration with only four variables. The microplates are assumed made of functionally graded (FG) composites, the material properties of which are changed continuously through the variable thickness. The variation of microplate thickness obeys three different schemes including linear, concave, and convex ones. It is highlighted that by changing the pattern of the thickness variation from convex type to linear one, and then from linear type to concave one, the both classical and couple stress continuum-based nonlinear frequency of the microplates having different shapes increases due to a higher value of the average plat thickness. On the other hand, by considering this change in the thickness variation pattern, it is seen that the significance of the couple stress size effect increases. For this reason, the significance of the stiffening scheme associated with the gradient of rotation gets lower through increment of the material gradient index of a FG composite microplate.

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