Generalization of conservative nonlinear normal modes to the non-conservative equation of motion

International audienceThis work presents a method for calculating non-conservative Nonlinear Normal Modes (NNMs) based on the conservative NNMs. A specific fictional force is added to the initial non-conservative equation of motion in order to insure the energy balance of the damped nonlinear equation. By doing so, conservative equations corresponding to Phase and Energy resonances are obtained. Therefore non-conservative NNMs can be computed with conservative NNMs calculation methods. Finally, the proposed method allows to calculate all non-conservative NNM branches with their stability and bifurcation points. INTRODUCTION The literature comprises several publications about the computation of conservative NNMs, see for example [1]. In [2], the Harmonic Balance Method (HBM), a specific phase condition, Lagrange multipliers and a modified quadratic eigenvalue problem are used to compute periodic solutions, stability and bifurca-tion points. Some researches concern on the influence of damping on the NNM. In [3], an energy balance is applied to conservative NNMs to explore the connection between NNMs and damped frequency responses. In [4], Krack introduced a fictional negative damping to insure energy balance. In the present work, the energy balance is insured by a fictional force that preserves the underlying invariant manifold. Two cases are distinguished, namely NNMs corresponding to phase and energy resonances