Non-linear modes of vibration of thin cylindrical shells in composite laminates with curvilinear fibres

A formulation applicable to free, periodic, geometrically non-linear vibrations of thin shallow shells made of composite layers with curvilinear fibres is presented. The modes of vibration of this type of Variable Stiffness Composite Laminated (VSCL) shallow shells are examined in the non-linear regime. Due to the membrane effects and their coupling with bending, the modes of vibration of VSCL shells are more affected by alterations in the curvilinear fibre paths than what was previously found to occur in plates. Indeed, it is discovered that by changing one of the parameters that defines the fibre path – keeping all other properties of the shells unaltered – the degree of softening can be changed, hardening can become softening, the vibration displacement amplitude at which turning points occur can change and the amplitudes of harmonics vary. A significant deduction, which results from the numerical tests, is that modes of vibration that have mode shapes with more half-waves are less likely to experience softening. A geometric explanation for this behaviour, which does not apply only to VSCL shells, is given.