This paper investigates a cantilever beam nonlinear dynamic behaviour, on which the nonlinearity is introduced with permanent magnet interactions or with a non-holonomic contact. The experimental time domain responses obtained from non-zero initial conditions are measured using a laser profilometer, conventionally adopted for product shape detections in online industrial applications. The Fourier transform, Continuous Wavelet transform, and Hilbert transform are used to investigate nonlinear phenomena in the frequency content, highlighting advantages and drawbacks of the three methods in catching instantaneous phenomena. Then, a Multi-Phi approach is proposed to describe the time evolution of nonlinear systems by means of a discrete number of linearised systems. Therefore, two linearised models have been developed and tuned to describe the dynamic behaviour of different Euler–Bernoulli cantilever beam configurations. The experimental data of nonlinear systems are compared with the corresponding ones of the linear system to evaluate the effects of introduced nonlinearities on the overall dynamic properties.

The development of rotordynamic systems with reduced energy dissipation is a key challenge in modern applications, such as Flywheel Energy Storage Systems. This paper investigates a fully passive vertical rotor system supported by two passive magnetic bearings whose configuration provides radial stability while minimising power losses due to their thrust effect. A numerical model describes the forces and stiffness of the magnetic bearings, identifying the operational range of the thrust–radial support configuration. A test rig is developed for the experimental characterisation of the rotor and passive magnetic bearings in both static and dynamic conditions. Different magnetic thrust force levels are tested by varying the axial distance between the rotor and stator magnetic rings of the bearings. Static tests are performed to measure the weight force compensation corresponding to the different bearing configurations, validating the numerical model. Dynamic tests analyse the rotor power losses with a non-invasive approach via optical sensor measurements.