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Carbon nanotubes are well known for their exceptional mechanical properties which make them an ideal candidate for reinforcing applications in the polymer matrix. This work presents the study of vibration and damping analysis of such nanocomposite shell structures. A Mori-Tanaka based micromechanical model has been developed to evaluate the time and frequency-dependent viscoelastic properties of such composites. The obtained viscoelastic properties have been used for vibration study of various shell structures by developed eight noded shell element having five degree of freedom at each node based on the Mindlin’s hypothesis. The effects of the interfacial parameters on time and frequency response of such structures have also been studied. Results show that the elastic properties, as well as damping properties of nanocomposite structures can be improved with the addition of CNTs