Free vibration of square laminates with delamination around a central cutout using HSDT

A finite element formulation based on Higher Order Shear Deformation Theory and Hamilton's principle is developed to study the free vibration response of thick square composite plates having a central rectangular cutout, with and without the presence of a delamination around the cutout. An attempt is made to gain a complete understanding of the effect of a rectangular cutout on natural frequencies of the laminate. The concept of a frequency envelope is found to be quite convenient for this purpose. A systematic study is carried out to investigate the effect of material orthotropy, boundary conditions and side-to-thickness ratio on the free vibration response. In addition, effects of delamination size and its location around the cutout on the natural frequency of a thick square laminate are examined. A comparison is also made between results obtained using First Order Shear Deformation Theory and Higher Order Shear Deformation Theory.