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In this work, the dynamic characteristics of composite damping sandwich open conical shells are investigated. Considering the superposition effect of rotational inertia and shear deformation during structural vibration, the expressions of kinetic energy and strain energy of composite damping sandwich open conical shell (CDSOCS) are derived based on the first-order shear deformation theory. The Rayleigh-Ritz method is used to establish the free vibration equations for thin and medium-thickness shells. According to the simply supported boundary conditions, the Navier double series method is used to solve the vibration equation. The theoretical solution is compared with the previous results and ANSYS finite element simulation results, and the rationality and effectiveness of the theoretical calculation model are verified. The influence of the thickness change of the sandwich layer under different laying angles and the position change of the sandwich layer under different thickness-diameter ratios on the dynamic characteristics of the CDSOCS is discussed, which provides a reference for the design of orthotropic composite damping sandwich complex structures. [ABSTRACT FROM AUTHOR]