On the Motion of Harmonically Excited Spring Pendulum in Elliptic Path Near Resonances

被引:42
作者
Amer, T. S. [1 ]
Bek, M. A. [2 ]
Hamada, I. S. [1 ]
机构
[1] Tanta Univ, Fac Sci, Dept Math, Tanta 31527, Egypt
[2] Tanta Univ, Fac Engn, Dept Phys & Engn Math, Tanta 31734, Egypt
关键词
ASYMPTOTIC ANALYSIS; CHAOTIC RESPONSES; DYNAMICS; SYSTEM;
D O I
10.1155/2016/8734360
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The response of a nonlinear multidegrees of freedom (M-DOF) for a nature dynamical system represented by a spring pendulum which moves in an elliptic path is investigated. Lagrange's equations are used in order to derive the governing equations of motion. One of the important perturbation techniques MS (multiple scales) is utilized to achieve the approximate analytical solutions of these equations and to identify the resonances of the system. Besides, the amplitude and the phase variables are renowned to study the steady-state solutions and to recognize their stability conditions. The time history for the attained solutions and the projections of the phase plane are presented to interpret the behavior of the dynamical system. The mentioned model is considered one of the important scientific applications like in instrumentation, addressing the oscillations occurring in sawing buildings and the most of various applications of pendulum dampers.
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页数:15
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