Nonlinear Dynamics

, Volume 50, Issue 4, pp 841–847

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


  • M. R. Bolla
    • Space Mechanics and Control DivisionNational Institute for Space Research (INPE)
    • Department of Applied MathematicsState University of São Paulo at Rio Claro
  • J. L. P. Felix
    • Department of Exact Sciences and Earth – URIUniversidade Integrada do Alto Uruguai e das Missões, CEP
  • D. T. Mook
    • Department of Engineering Sciences and MechanicsVirginia Tech
Original Paper

DOI: 10.1007/s11071-007-9232-3

Cite this article as:
Bolla, M.R., Balthazar, J.M., Felix, J.L.P. et al. Nonlinear Dyn (2007) 50: 841. doi:10.1007/s11071-007-9232-3


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 vibrationsSommerfeld effectAnalytical solution

Copyright information

© Springer Science+Business Media, Inc. 2007