Vibration of functionally graded material plates with cutouts & cracks in thermal environment

TL;DR

This study investigates how cutouts, cracks, and thermal environments influence the vibration behavior of functionally graded material plates, using advanced numerical methods to capture discontinuities and singularities.

Contribution

It introduces a mesh-independent partition of unity method framework with enriched elements to analyze vibrations of FG plates with cutouts and cracks in thermal settings.

Findings

Vibration characteristics are significantly affected by cutout and crack geometry.

Thermal gradients alter the stiffness and natural frequencies of the plates.

Boundary conditions influence the vibration response in the presence of discontinuities.

Abstract

In this paper, the effect of a centrally located cutout (circular and elliptical) and cracks emanating from the cutout on the free flexural vibration behaviour of functionally graded material plates in thermal environment is studied. The discontinuity surface is represented independent of the mesh by exploiting the partition of unity method framework. A Heaviside function is used to capture the jump in the displacement across the discontinuity surface and asymptotic branch functions are used to capture the singularity around the crack tip. An enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction. The effective properties of the functionally graded material are estimated using the Mori- Tanaka homogenization scheme and the plate kinematics is based on the first order shear deformation theory. The influence of the plate geometry, the geometry of the cutout, the crack length, the thermal gradient and the boundary conditions on the free flexural vibration is numerically studied.