Semi-analytical solutions for free vibration of anisotropic laminated plates in cylindrical bending

Elasticity solutions for free vibration of angle-ply laminates subjected to cylindrical bending are obtained using a newly developed semi-analytical approach. The thickness domain is solved analytically using the transfer matrix method based on the state space concept, while the in-plane domain is solved approximately via the technique of differential quadrature. The present method is applicable to arbitrarily thick laminates and for treating arbitrary edge conditions. The method is verified by comparisons with the exact solutions of Pagano's problem. Effects of variation of ply angle on the vibration properties of laminates are investigated; mode shape switching is observed when ply angle varies. Numerical results for fully clamped thick laminates are presented for future references.