ROTARY INERTIA, AXIAL AND SHEAR DEFORMATION EFFECTS ON THE IN-PLANE NATURAL FREQUENCIES OF SYMMETRIC CROSS-PLY LAMINATED CIRCULAR ARCHES

Abstract

The in-plane free vibrational analysis of symmetric cross-ply laminated circular arches is studied using both the Timoshenko and Bernoulli–Euler beam theories. The free vibration equations are derived based on the distributed parameter model. The transfer matrix method is used in the analysis. The numerical algorithm available in the literature is adopted to compute the exact overall dynamic transfer matrix of the curved beam. The rotary inertia, axial and shear deformation effects are considered in the Timoshenko analysis by the first-order shear deformation theory. All these effects are neglected in the Bernoulli–Euler analysis. Radius of the arch/thickness ratios from 5 to 25, fixed–fixed, fixed–simple and fixed–free boundary conditions, and two values of the opening angles (10° and 90°) are taken into consideration in the parametric study. The effects of the ratio of the extensional modulus to the transverse modulus on the natural frequencies are examined. Non-dimensional numerical results are also presented in terms of relative errors.