The free vibration behavior of carbon fiber quasi-isotropic laminates containing a center hole with free-clamped boundary conditions is investigated numerically and analytically; the results are validated through subsequent experimentation. Different finite element models based on classical plate theory (Kirchhoff) and the shear deformable theory (Mindlin) within the framework of equivalent single-layer and layer-wise concepts as well as the three-dimensional theory of elasticity are developed. These models are created using the finite element software Abaqus to determine the natural frequencies and the corresponding mode shapes. In addition, an analytical model based on Kirchhoff plate theory is developed. Using this analytical model, an equivalent bending-torsion beam model for cantilever laminated plate is extracted taking into account the reduction in local stiffness and mass induced by the center hole. Experimental vibration analyses are carried out using an optic-based vibration measurement tool to extract the frequency response functions (FRFs) and to measure the natural frequencies. Numerical and analytical frequency values computed from different models are then compared with those obtained through experimental vibrational tests and the accuracy of each FE and analytical model type is assessed. It is shown that very good agreements are obtained between the estimated natural frequencies using the analytical, FE models, and their experimental counterparts.
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