A new formulation for the existence and calculation of nonlinear normal modes

By S. Bellizzi, R. Bouc. 2005

51 citations recorded by the source corpus.

A new formulation is presented here for the existence and calculation of nonlinear normal modes in undamped nonlinear autonomous mechanical systems. As in the linear case an expression is developed for the mode in terms of the amplitude, mode shape and frequency, with the distinctive feature that the last two quantities are amplitude and total phase dependent. The dynamic of the periodic response is defined by a one-dimensional nonlinear differential equation governing the total phase motion. The period of the oscillations, depending only on the amplitude, is easily deduced. It is established that the frequency and the mode shape provide the solution to a 2π-periodic nonlinear eigenvalue problem, from which a numerical Galerkin procedure is developed for approximating the nonlinear modes. The procedure is applied to various mechanical systems with two degrees of freedom.

Subfields: Civil and Structural Engineering, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b2aa4677815c39d77b4844035241a1f140815ee7

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In Civil and Structural Engineering

In Control and Systems Engineering

Citations in the corpus

Numerical computation of nonlinear normal modes in mechanical engineering (2016, background): “Another interesting approach was proposed by Bellizzi and Bouc, first for conservative systems [105] and then for nonconservative systems [114].”
Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures (2006, background): “[17,35] is here considered, where modal damping have been added to each equation.”
Nonlinear normal modes, Part I: A useful framework for the structural dynamicist (2009, methodology): “A method similar in spirit to the harmonic balance method and to the Galerkin-based approach in [48] was introduced in [41,90].”