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Vibration suppression of non-linear system via non-linear absorber
Faculty
Science
Year:
2008
Type of Publication:
Article
Pages:
1948-1963
Authors:
Amer, Y. A, El-Sayed, A. T
DOI:
10.1016/j.cnsns.2007.04.018
Journal:
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION ELSEVIER SCIENCE BV
Volume:
13
Research Area:
Literature; Mathematics; Mechanics; Physics
ISSN
ISI:000255537300022
Keywords :
vibration control, response function, resonance, multi-excitation, stability
Abstract:
In this paper, the coupled non-linear differential equations of the non-linear dynamical two-degree-of-freedom vibrating system including quadratic and cubic non-linearities are studied. The system consists of the main system and the absorber. The absorber is used to control the main system vibrations when subjected to multi-external excitation forces at simultaneous primary and internal resonance. This system represents many applications in machine tools, ultrasonic cutting process, etc. The method of multiple scales perturbation technique (MSPT) is applied throughout to determine the solution up to third order approximations. The different resonance cases are reported and studied numerically. Stability is studied applying frequency response functions. The effects of different parameters of the system are studied numerically. Optimum working conditions for the absorber where obtained at internal resonance ratio 1:3. This means smaller mass for the absorber which solves the problem of space limitation. A comparison is made with the available published work. (c) 2007 Elsevier B.V. All rights reserved.
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