| Schauder fixed point theorem based existence of periodic solution for the response of Duffing’s oscillator Ahmad Feyz Dizaji
The Journal of Mechanical Science and Technology, vol. 23, no. 8, pp.2299-2307, 2009
Abstract : 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.
Keyword :
Banach’s theorem; Large deformation of thin plates; Moving loads; Non-linear vibration; Schauder fixed point theorem
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