... forces acting on the bearings is based on solving the Reynolds equation and taking cavitation into account. Lagrange equations of the second kind and the principle of virtual work are used to derive equations of motion. The Runge–Kutta method with an adaptive time step is applied for their solution...

... 2008 magnetic bearings mechanical stability nonlinear differential equations oscillations rotors Runge-Kutta methods vibrations active magnetic bearings combined resonance periodic time-varying stiffness Active magnetic bearings (AMBs) are being increasingly used...

...M. Zidi In this paper, we study the combined torsion, circular and axial shearing of a compressible hyperelastic and prestressed tube. The analysis is carried out for a class of Ogden elastic material and the governing nonlinear equations are solved numerically using the Runge-Kutta method...