Free vibration analysis of FGM plates with complex cutouts by using quasi-3D isogeometric approach

Abstract

This study intends to analyze free vibration response of functionally graded material (FGM) plates with complex cutouts. Isogeometric analysis (IGA) method combined with a new quasi-3D higher-order shear deformation theory (HSDT) for the vibration analysis is presented to predict the dynamic behavior. The quasi-3D HSDT is able to account for transverse shear and normal deformations with only four unknown variables using the dissimilar shear and normal shape functions. In the refined quasi-3D hybrid type HSDT, the fully 3D material matrix is employed in the stress–strain relations, and the governing equations for the dynamic problem are derived through the Hamilton's principle. Validity of the present quasi-3D isogeometric approach is investigated by testing several numerical examples in the open literature and comparing the predicted results with the available reference solutions. It can be concluded that the proposed analysis method is accurate and effective in solving free vibration behavior of FGM plates with complex cutouts. Illustrative examples are also given to examine the effects that the ingredient fraction, plate geometric parameter and boundary condition have on the free vibration behavior. Results demonstrate that there exists a critical plate length-to-thickness ratio above which the natural frequency of the perforated FGM plate does not increase any more even though the ratio becomes larger.