Non-Linear Analysis of Vibrations of Non-Linear System Subjected to Multi-Excitation Forces via a Non-Linear Absorber

Abstract

The dynamic response of mechanical and civil structures subjected to high-amplitude vibration is often dangerous and undesirable. Sometimes controlled vibration is desirable as in the machinery used in the formation of rigid hard material as Ceramics and diamond. This process is done via the passive control methods. The main purpose of this paper is to how reduction of vibration of nonlinear system subjected to multi-excitation forces via a nonlinear absorber. The nonlinear differential equations describing the model, which describe ultrasonic cutting machine are solved by using perturbation method. The effects of different parameter on the response of the system are studied. The stability of the numerical solution is investigated by using frequency response equations and phase-plane method. The simulation results are achieved using Matlab and Maple programs. A comparison is made with the available published work.

The dynamic response of mechanical and civil structures subjected to high-amplitude vibration is often dangerous and undesirable. Sometimes controlled vibration is desirable as in the machinery used in the formation of rigid hard material as Ceramics and diamond. This process is done via the passive control methods. The main purpose of this paper is to how reduction of vibration of nonlinear system subjected to multi-excitation forces via a nonlinear absorber. The nonlinear differential equations describing the model, which describe ultrasonic cutting machine are solved by using perturbation method. The effects of different parameter on the response of the system are studied. The stability of the numerical solution is investigated by using frequency response equations and phase-plane method. The simulation results are achieved using Matlab and Maple programs. A comparison is made with the available published work.

Cite this paper

T. El-Ghareeb, Y. Hamed and M. Abd Elkader, "Non-Linear Analysis of Vibrations of Non-Linear System Subjected to Multi-Excitation Forces via a Non-Linear Absorber,"*Applied Mathematics*, Vol. 3 No. 1, 2012, pp. 64-72. doi: 10.4236/am.2012.31011.

T. El-Ghareeb, Y. Hamed and M. Abd Elkader, "Non-Linear Analysis of Vibrations of Non-Linear System Subjected to Multi-Excitation Forces via a Non-Linear Absorber,"

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