effects of asymmetric stiffness on parametric instabilities of rotor

this work deals with effects of asymmetric stiffness on the dynamic behaviour of the rotor system. the analysis is presented through an extended lagrangian hamiltonian mechanics on the asymmetric rotor system, where symmetries are broken in terms of the rotor stiffness. the complete dynamics of asymmetries of rotor system is investigated with a case study. in this work, a mathematical model is developed considering symmetry breaking of a finite rotor due to stiffness. the natural frequency and amplitude of the rotor are obtained analytically through extended lagrangian formulation. the asymmetries in rotor are also modeled through bond graph modeling technique for the computational analysis.  the simulation result shows a considerable agreement with the analytical results.  the limiting dynamics of rotor is shown and analyzed through simulation.