Free vibration analysis of cantilever open-hole composite plates

The free vibration behavior of quasi-isotropic carbon fiber laminated composite plates containing circular holes with free-clamped boundary conditions are numerically, analytically, and experimentally investigated. 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 approach, an equivalent bending-torsion beam model for cantilever laminated plates 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 optically-based vibration measurement tool to extract the frequency response functions and to measure the natural frequencies. Numerical and analytical natural frequency values are then compared with those obtained through experimental vibrational tests, and the accuracy of each finite element (FE) and analytical model type is assessed. It is shown that the natural frequencies obtained using the analytical and FE models are within 8% of the experimentally determined values.