An analytical method is presented to determine the dynamic response of a coupled flexural and torsional vibration of composite beams. The general governing equations of motion are presented and a closed form solution for free vibration of the composite beam that demonstrates both geometric and material coupling is developed. The proposed solution is used to compute the natural frequencies, modal loss factors, and mode shapes of the composite beam for several modes of the coupled bending and torsional vibrations for any boundary conditions. In this analysis, hysteretic damping for the composite beam is considered and its effects on mode shapes and modal loss factors are determined. In addition, the variation of modal parameters such as bending displacement, bending slope, torsional rotation, shear force, bending moment, and torque along the beam for the first four mode shapes are presented for the clamped-free boundary conditions. Moreover, to verify the validity of the presented analytical method, results for the cases with no damping are compared with the previously established results and good agreement is achieved. The presented results can provide a guideline for selecting appropriate geometries and materials to design composite beams.

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