A nonlinear viscous damper is a type of damping device used in engineering to dissipate energy and reduce vibrations in structures. Damping is essential in many engineering applications to control the response of structures subjected to dynamic loads, such as earthquakes, wind, or machinery-induced vibrations. In a nonlinear viscous damper, the damping force is not directly proportional to the velocity of the structure, which distinguishes it from linear viscous dampers. The nonlinearity in the damping force-velocity relationship can be designed to provide specific performance characteristics. The main reasons for employing nonlinear viscous dampers include increased energy dissipation - nonlinear viscous dampers can provide higher energy dissipation compared to linear dampers, making them effective in controlling larger vibrations. This work deals with numerical analysis of a single degree of freedom dynamical system representing plate-flow interaction with quadratic drag force subjected to harmonic excitation with and without additional impacts during oscillations. Numerical analysis is based on the bifurcation theory. The theory focuses on understanding the qualitative changes in the behaviour of a system as a parameter is varied. Without additional stoppers the system behaves as a linear system. With “soft” stoppers the system gets limited displacements with the same velocities, multiplicity and more uniform distribution of amplitudes of oscillations. Understanding bifurcations is crucial in predicting and controlling the behaviour of dynamic systems, especially when dealing with nonlinear phenomena.