Common effects of the rotary inertia and shear deformation on the out-of-plane natural frequencies of composite circular bars

A numerical study is performed to investigate the common effects of the rotary inertia and shear deformation on the first six out-of-plane free vibration frequencies of symmetric cross-ply laminated circular bars with the help of the transfer matrix method. The distributed parameter model is employed in the free vibration analysis of the vibrating system. The overall transfer matrix is computed up to any desired accuracy using the effective numerical algorithm available in the literature. The first order shear deformation theory called as Timoshenko model is included in the analysis. For the opening angle alpha = 90 degrees, the effects of the rotary inertia and shear deformation are examined and presented in graphical forms considering boundary conditions (clamped-free, clamped-simple and clamped-clamped), and the slenderness ratios (R/h = radius of the arch/thickness of the rectangular section = 5-25). The effects of the ratio of the extensional modulus to the transverse modulus on the natural frequencies are also examined. (C) 2001 Elsevier Science Ltd. All rights reserved.