Several approaches are typically used to reduce torsional vibrations in mechanical systems with piston-driven engines [14,15]. Various types of f lexible couplings and dual-mass f lywheels are widely implemented [16][17]. It has been demonstrated that pneumatic tuners with adjustable torsional stiffness can be used to achieve active tuning of torsional vibrations [19][20][21][22][23]. Certain research ventures have focused on the application of nonlinear energy sink (NES) [24] and targeted energy transfer (TET) [25] with the goal of designing a device with quasi-zero torsional stiffness [26]. These research avenues require new approaches to solving analytical models. It is common practice in engineering that complicated systems are simplified -e.g. nonlinear systems are often linearised around an operating point. While in some cases linearisation is adequate as demonstrated in [27][28][29], there are applications that require nonlinear models because linearisation either does not provide sufficient accuracy, or is not possible at all [30].The first step in extending the linear model is the addition of a cubic term. Such a system, governed by the Duffing equation, has been the subject of numerous analyses [31]. Extensive mathematical tools have been developed to model the system, whether the nonlinearity is weak or strong.In this presented work, we decided to focus on a different type of a nonlinear system. Systems with power-law restoring force have not been extensively studied, in spite of the fact that they may occur naturally in many engineering problems. The source of nonlinearity can be contact law, such as Hertzian potential, for which restoring force f varies with displacement q as f ∝ q 1.5 . Further examples include systems without pre-tension or systems tuned to zero stiffness around the operating point. If the force-carrying medium is gas, such as in the pneumatic tuners [18], the restoring force is also inherently nonlinear with power-law dependence.