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ISSN 1025-6415. Dopov. Nac. acad. nauk Ukr. 2017. No 10 © A.N. Timokha, I.A. Raynovskyy, 2017 An upright circular cylindrical rigid tank performs a small-magnitude prescribed periodic horizontal motion, which is described by the two generalized coordinates 0 1( ) r t η and 0 2( ) r t η ( 0 r is the tank radius) as shown in fig. 1. Those tank motions are relevant for bioreactors [1]. In contrast to industrial containers whose dimensions are relatively large, the bioreactors have 0 5 10 r ≈ − [cm] that requires accounting for the damping associated with a laminar boundary layer and the bulk viscosity. The problem is studied in the nondimensional statement provided by the characteristic size

The damped sloshing in an upright circular tank due to an orbital forcing