An analytical study of the effects of transverse shear deformation and anisotropy on natural vibration frequencies of laminated cylinders

Abstract

Natural vibration frequencies of orthotropic and anisotropic simply supported right circular cylinders are predicted using a higher-order transverse-shear deformation theory. A comparison of natural vibration frequencies predicted by first-order transverse-shear deformation theory and the higher-order theory shows that an additional allowance for transverse shear deformation has a negligible effect on the lowest predicted natural vibration frequencies of laminated cylinders but significantly reduces the higher natural vibration frequencies. A parametric study of the effects of ply orientation on the natural vibration frequencies of laminated cylinders indicates that while stacking sequence affects natural vibration frequencies, cylinder geometry is more important in predicting transverse-shear deformation effects. Interaction curves for cylinders subjected to axial compressive loadings and low natural vibration frequencies indicate that transverse shearing effects are less important in predicting low natural vibration frequencies than in predicting axial compressive buckling loads. The effects of anisotropy are more important than the effects of transverse shear deformation for most strongly anisotropic laminated cylinders in predicting natural vibration frequencies. However, transverse-shear deformation effects are important in predicting high natural vibration frequencies of thick-walled laminated cylinders. Neglecting either anisotropic effects or transverse-shear deformation effects leads to non-conservative errors in predicted natural vibration frequencies