An analytical solution is presented to predict the sloshing response of a cylindrical liquid storage tank with a floating roof under seismic excitation. The contained liquid is assumed to be inviscid, incompressible and irrotational, while the floating roof is idealized as an isotropic elastic plate with uniform stiffness and mass. The dynamic interaction between the floating roof and the liquid is taken into account exactly within the framework of linear potential theory. By expanding the response of the floating roof into free vibration modes in air and employing the Fourier-Bessel expansion method in cylindrical coordinates, the solution is obtained in an explicit form which is useful for parametric understanding of the sloshing behavior and preliminary study in the early design stage. Numerical results are also provided to investigate the effect of the stiffness and mass of the floating roof on the sloshing response.

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