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The laminar flow around heaving axisymmetric and three-dimensional cylinders with damping plates is numerically studied for various Keulegan-Carpenter numbers. The Navier-Stokes equations are solved using OpenFOAM, which is applied to the flow on a moving mesh. For processing of results the semi-empirical Morison equation is used. Calculations are conducted for one cylinder, one cylinder with one disk, one cylinder with two disks, and one cylinder with one pentagonal plate. The calculated values are compared against experimental data.