Geometrically Non-linear Free Vibration of Fully Clamped Symmetrically Laminated Composite Skew Plates

The present work concerns the geometrically non-linear free vibration of fully clamped symmetrically laminated composite skew plates. The theoretical model based on Hamilton's principle and spectral analysis previously applied to obtain the non-linear mode shapes and resonance frequencies of thin straight structures, such as beams, plates and shells is used. A convergence study has been performed and has shown that 18 plate functions should be taken into account. Results are given for the linear and non-linear fundamental mode shape of fully clamped symmetrically laminated composite skew plates, considering different parameters such as the skew angle, the number of layers, the fiber orientation, the vibration amplitudes and plate aspect ratio. It was found that the non-linear frequencies increase with increasing the amplitude of vibration and increasing the skew angle, which corresponds to the hardening type effect, expected in similar cases, due to the membrane forces induced by the large vibration amplitudes.