In this paper the free vibration of a two-degree-of-freedom system are considered. Two equal masses are connected with a truly nonlinear elastic spring and each of them with an elastic element with a fixed and unmovable end. Due to initial displacement the free vibrations of both bodies in the system occur. The motion is described with a system of two coupled second order differential equations with nonlinearities whose order is any positive rational number (integer or non-integer) with value not smaller than 1. Using an appropriate transformation, the system is separated into two uncoupled differential equations whose solution is obtained analytically. In general, the vibration of masses is described with a trigonometric and an Ateb special function. In differential equations of motion small nonlinear terms appear. A solution procedure for solving strong nonlinear differential equations with additional small nonlinearity is developed. The method is based on the perturbed version of solution of the strong nonlinear differential equation. The averaging over the period of functions is introduced. The method is applied for a system where the connection between masses is with strong quadratic nonlinearity. Analytically obtained results are compared with numerical ones. Solutions agree well.
Nonlinear vibrations of a symmetrically supported two-degree-of-freedom system
10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 ; 2014 ; Narvik, Norway
AIP Conference Proceedings ; 1637 , 1 ; 253-260
10.12.2014
8 pages
Aufsatz (Konferenz)
Elektronische Ressource
Englisch
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