Multi-absorbers for vibration control of non-linear structures to harmonic excitations (Part I: response, stability, chaos and effects of different parameters)

Vibrations and dynamic chaos should be controlled in either structures or machines. The most famous method of vibration control is using absorbers or dampers or neutralizers. The main problem in using such devices is the variable frequency of the excitation source, while the absorber is usually designed to control one frequency always at primary resonance where damage of the system is probable. In this paper we suggest to use multi-absorbers for vibration control of a structure or machine table which is simulated by a second order non-linear mechanical system having both quadratic and cubic non-linearities, subjected to harmonic excitation. The multiple time scale perturbation technique is applied throughout. An approximate solution is derived up to and including the third order approximation for a system containing multi-absorbers. As an example, we used a second order non-linear system having two absorbers working at two different excitation frequencies. In Part I, the effects of the main system parameters have been investigated numerically and from the frequency response equation. Many resonance cases have been deduced. In Part II, most of them are tested numerically to obtain the optimum working conditions for such system. The end of this work gives some design recommendations. (author)