## 1 Introduction
[PERSON] [14] characterized a magnetorheological fluid damper and performed a quarter car analysis with it. Research on the control of the MR damper for two-wheeler applications was carried out by [PERSON] et al. [15]. An example of the application of MR dampers in technological machinery is given in the research work carried out by [PERSON] et al. [16]. The effect on chatter vibration suppression in straight turning operation is investigated using Multiphysics simulation software (Version: COMSOL 5.5) for the process simulation. The tests proved the efficiency of the developed damper. The Multiphysics coupling simulation model and the circuit simulation model were used by [PERSON] et al. [17] to develop MR dampers for anti-seismic buildings. The applied multi-objective structural optimization enabled the improvement of the output damping force by 6.6% and the adjustable range of the damper by 46.3%. [PERSON] et al. [18] integrated computational fluid mechanics (CFD) and finite element analysis (FEA) to investigate the dynamic characteristics and the controllable damping force of shear-mode MRP (magnetorheological plastomer) dampers. A number of studies present the development of nonlinear dampers using shear thickening fluids (STFs). The viscosity of these fluids increases with the increase in shear rate. Article [19] presents an analysis of the structure and the phenomena of shear thickening in fluids, provides a phenomenological model of STFs, and gives examples of typical applications, including personal protection, preventing spike puncture, cutting knives, impact suppression and vibration control. [PERSON] et al. [20] present a phenomenological model showing the relationship between complex viscosity and dynamical shear rate. The effectiveness of STF is demonstrated in a cylinder-shaped damper with STF. The particular features of the damper are that after reaching the critical value of shear rate, the damping force stops increasing and the damper is sensitive to the annular gap. [PERSON] & [PERSON] [21] developed an analytical model to predict the damping characteristics of dampers with non-Newtonian fluids, including STF. An analysis based on laminar Poiseuille flow was performed to study the annual gap and holes in the piston of a cylinder-shaped damper. The analytical solution was validated by CFD analysis. The effectiveness of the damper was demonstrated on a single-degree-of-freedom (DOF) mass-spring-damper system by plotting its amplitude frequency characteristics. In summary, it can be stated that with the application of nonlinear dampers, damping effectiveness in dynamical systems can be achieved over significantly wider excitation frequency ranges than with linear systems. Nonlinear systems are developed as passive and active (or semi-active) controllable systems. Typically, passive systems include several interacting components of complicated geometry. They can be very effective, but their development needs innovative solutions and a deep understanding of dynamical phenomena in order to obtain a precise matching of the structural, physical and mechanical parameters necessary to achieve effective performance characteristics. Active systems are sophisticated systems for which proper control strategies need to be developed. In this research, the results of the development of a nonlinear passive damper of an original structure named the nonlinear slit membrane damper are presented. The structure is of simple geometry compared with the majority of reported developments of passive and active dampers. Its key component is the slit membrane. The behavior of the membrane under external dynamical loads is the reason for the nonlinear damping characteristic and damping effectiveness.