Free Vibration Analysis of Laminated Composite Plate with a Cut-Out

This study investigates the free vibration behaviour of simply supported square laminated composite plates with a square cut-out and straight fibre orientation designs. The cut-out is placed at the centre of the plate. Different cases are considered with fibre angles changed from $${0}^{\circ }$$ to $${45}^{\circ }$$ , at an interval of $${5}^{\circ }$$ . The analytical method based on the first-order shear deformation laminate theory (FSDT) and the numerical method are both applied to obtain the free vibration properties in terms of the natural frequencies and mode shapes. The results obtained from these two methods are compared for verification. The effects of the cut-out size and fibre angles on the mode shapes are studied. It is found that the natural frequencies are influenced substantially by the size of cut-out and the fibre orientation, which can also be used to modify the mode shape and nodal line locations for the purpose of vibration suppression. With increasing the size of the cut-out of a square plate, the $${3}^{\mathrm{rd}}$$ natural frequencies of the structure generally decrease. It is shown that the $${2}^{\mathrm{nd}}$$ natural frequency increases with fibre angle increasing from $${0}^{\circ }$$ to $${45}^{\circ }$$ . The mode shape can also be tailored by the design of the fibre angle with the nodal line changing from being approximately the horizontal to the diagonal of the plate. The study provides some enhanced understanding on the free vibration properties of the laminated composite plate with a cut-out to achieve better dynamic designs.