Vibration analysis of multi-rotor system through extended Lagrangian formalism∗

This work deals with the applications of extended Lagrangian-Hamiltonian mechanics on the asymmetric multi rotor system, where the symmetries are broken due to rotor mounted on the shaft with different masses and dimensions. The whole dynamics of asymmetries of multi-rotor system is investigated through extended Lagrangian formalism with a case study. In this work, an analytical model through extended LagrangianHamiltonian approach is developed considering a two-rotor system with different masses. The amplitude and natural frequency of the multi-rotor system are determined analytically. The multi-rotor system is modeled through bond graph modeling techniques as it brings the unified modeling approach in several energy domain. Symbol-shaktir software is used for the simulation of the model. The effects of the mass of the rotor system on the amplitudes and frequencies are analyzed using numerical simulations. It is further observed that amplitude of the rotor increases with the mass of the rotors, which are also affirmed theoretically.