On the Use of the Multiple Scale Harmonic Balance Method for Nonlinear Energy Sinks Controlled Systems

  • Angelo Luongo
  • Daniele Zulli
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 168)


The Multiple Scale Harmonic Balance Method (MSHBM) is discussed here for several paradigmatic systems (primary structures) equipped with a Nonlinear Energy Sink (NES). This is a small-mass oscillator with essentially nonlinear stiffness, used for passive control purpose. The method permits to overcome the difficulties inherent to standard perturbation methods, which occur as a consequence of the nonlinearizable nature of the NES equation. It combines the Multiple Scale Method and the Harmonic Balance Method to furnish Amplitude Modulation Equations ruling the slow asymptotic dynamics of the augmented system. The MSHBM is illustrated here for a general, internally non-resonant, multi d.o.f. structure equipped with a NES and under multiple concurrent actions, namely steady wind inducing Hopf bifurcation , and 1:1 and 1:3 resonant harmonic forces. The relevant Amplitude Modulation Equations are specialized for simpler cases, where the single contributions of each external action is considered separately. The effect of the NES on the dynamics of the system is discussed for each case and numerical results are displayed.


Hopf Bifurcation Main System Nonlinear Energy Sink Subharmonic Resonance Galerkin Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was granted by the Italian Ministry of University and Research (MIUR), under the PRIN10-12 program, project No. 2010MBJK5B.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.M&MoCS—University of L’AquilaL’Aquila (AQ)Italy

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