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 rot ary inertia and shear deformation on the first six out-of-plane free vibrat ion frequencies of symmetric cross-ply laminated circular bars with the hel p of the transfer matrix method. The distributed parameter model is employe d in the free vibration analysis of the vibrating system. The overall trans fer matrix is computed up to any desired accuracy using the effective numer ical algorithm available in the literature. The first order shear deformati on theory called as Timoshenko model is included in the analysis. For the o pening angle alpha = 90 degrees, the effects of the rotary inertia and shea r deformation are examined and presented in graphical forms considering bou ndary conditions (clamped-free, clamped-simple and clamped-clamped), and th e 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 th e transverse modulus on the natural frequencies are also examined. (C) 2001 Elsevier Science Ltd. All rights reserved.