Free vibration analysis of composite foils with different ply angles based on beam theory

Previous investigations on composite materials are most based on uniform beam, while solid shape of foils are usually used in ocean and marine industries. To better predict the modal characteristics of composite solid foils, this paper modifies analytical model based on anisotropic thin-walled closed-section beam theory and investigates free vibration characteristics of the composite NACA0009 foil with different ply angles(θ). Good agreement has been obtained between the predicted natural frequencies and those simulated by Finite Element Method. Due to the non-coincidence of the shear center and mass center, the natural frequencies are not the same at opposite ply angles. The modal shapes illustrate the coupling of bending and torsion modes at different ply angles. For the first mode, the modal shapes are mainly the first bending with first torsion shape coupled at different ply angles. When |θ|<10°, the first torsion plays a key role in the second modal shapes, while when |θ|>10°, the main modal shapes of the second mode is changing to the second bending shape. Compared the results with and without coupling effects considered, the variation of natural frequencies may related to the change of modal shapes. By mode decomposition, it is shown that the percentages of uncoupling bending shapes and torsion shapes on each modal shapes with different ply angles.