A theoretical model, based on numerical simulations, is provided to analyze the properties of Frenkel excitons of strongly coupled aggregates such as columnar phases of liquid crystals or linear chains of J-aggregates. The effects of the degeneracy of the molecular transitions and of the orientational disorder in columnar phases on the delocalization behaviour and on the optical lineshapes of excitons are investigated. Considering the dynamic disorder in J-aggregate, it is shown that the intraband scattering and dephasing processes contribute, with increasing temperature, to the decrease of the number of coherently coupled molecules and to the lengthening of the exciton fluorescence lifetime.