Journal of Mechanical Science and Technology

, Volume 23, Issue 8, pp 2299–2307 | Cite as

Schauder fixed point theorem based existence of periodic solution for the response of Duffing’s oscillator

  • Ahmad Feyz Dizaji
  • Hossein Ali SepianiEmail author
  • Farzad Ebrahimi
  • Akbar Allahverdizadeh
  • Hasan Ali Sepiani


An initial-boundary value problem that is Duffing’s oscillator with time varying coefficients will be studied. Using Banach’s fixed-point theorem, the existence of periodic solution of the equation will be predicted. The method applied in this paper is the Schauder second fixed point theorem, which includes the response of structures under vibratory force systems. As an example, the dynamics of nonlinear simply supported rectangular thin plate under influence of a relatively moving mass is studied. By expansion of the solution as a series of mode functions, the governing equations of motion are reduced to an ordinary differential equation for time development vibration amplitude, which is Duffing’s oscillator. Finally, a parametric study is developed, after that some numerical examples are solved, and the validity of the present analysis is clearly shown.


Banach’s theorem Large deformation of thin plates Moving loads Non-linear vibration Schauder fixed point theorem 


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Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ahmad Feyz Dizaji
    • 1
  • Hossein Ali Sepiani
    • 1
    Email author
  • Farzad Ebrahimi
    • 1
  • Akbar Allahverdizadeh
    • 1
  • Hasan Ali Sepiani
    • 2
  1. 1.School of Mechanical EngineeringUniversity of TehranTehranIran
  2. 2.Department of Marine TechnologyAmirkabir University of TechnologyAmirkabirIran

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