Nonlinear Dynamics

, Volume 50, Issue 4, pp 841–847 | Cite as

On an approximate analytical solution to a nonlinear vibrating problem, excited by a nonideal motor

  • M. R. Bolla
  • J. M. Balthazar
  • J. L. P. Felix
  • D. T. Mook
Original Paper


This paper analyzes through Multiple Scales Method a response of a simplified nonideal and nonlinear vibrating system. Here, one verifies the interactions between the dynamics of the DC motor (excitation) and the dynamics of the foundation (spring, damper, and mass). We remarked that we consider cubic nonlinearity (spring) and quadratic nonlinearity (DC motor) of the same order of magnitude according to experimental results. Both analytical and numerical results that we have obtained had good agreement.


Nonideal vibrations Sommerfeld effect Analytical solution 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • M. R. Bolla
    • 1
  • J. M. Balthazar
    • 2
  • J. L. P. Felix
    • 3
  • D. T. Mook
    • 4
  1. 1.Space Mechanics and Control DivisionNational Institute for Space Research (INPE)São José dos CamposBrazil
  2. 2.Department of Applied MathematicsState University of São Paulo at Rio ClaroRio ClaroBrazil
  3. 3.Department of Exact Sciences and Earth – URIUniversidade Integrada do Alto Uruguai e das Missões, CEPSanto ÂngeloBrazil
  4. 4.Department of Engineering Sciences and MechanicsVirginia TechBlacksburgUSA

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