Vol-1 Issue-2 2015 IJARIIE-ISSN(O)-2395-4396 1165 www.ijariie.com 240 Study of Non-Linear Behavior of Vibrating System Chetan S.Dhamak 1 , Dipak S.Bajaj 2 , Vishnu S.Aher 3 , Kapil K. Dighe 4 1,2,3 Mechanical Engineering, Amrutvahini College of Engineering, Sangamner, Maharashtra, India ABSTRACT Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. In the case of the real structures a linear model will be insufficient to describe the dynamic behavior correctly. It thus appears natural to introduce non-linear models of structures which are able to predict the dynamic behavior of the real structures. This seminar includes study of non-linear vibrations, it different types and various applications. Here the vibratory behavior of an absorber of vibration related to a system subjected to a harmonic load, in the presence of uncertainties on the design parameters is optimised. The total system is modeled by two degrees of freedom (2 dof) with a shock absorber and a generalized non-linear stiffness. one proposes to optimize the vibratory behavior of an absorber of vibration related to a system subjected to a harmonic load, in the presence of uncertainties on the design parameters. The total system is modelled by two degrees of freedom (2 dof) with a shock absorber and a generalized non-linear stiffness. The resolution is carried out in the temporal field according to a traditional diagram. It is a question of seeking the optimal responses envelopes of the deterministic and stochastic case and this for the non-linear displacements, phases and forces. Keyword: - Non-Linear, Oscillation, Absorber and Vibration 1. INTRODUCTION Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point . In order to reduce the vibrations in the revolving machines and the mechanical systems, the dynamic absorbers are often used in various mechanical applications (Crankshaft, rotor of the wings of a helicopter, etc.). In the case of the real structures a linear model will be insufficient to describe the dynamic behavior correctly. It thus appears natural to introduce non-linear models of structures which are able to predict the dynamic behaviour of the real structures. The solutions of these non-linear problems are obtained by approximate methods which exploit iterative algorithms. In this paper, one proposes to optimize the vibratory behaviour of an absorber of vibration related to a system subjected to a harmonic load, in the presence of uncertainties on the design parameters. The total system is modeled by two degrees of freedom (2 dof) with a shock absorber and a generalized non-linear stiffness. The resolution is carried out in the temporal field according to a traditional diagram. It is a question of seeking the optimal responses envelopes of the deterministic and stochastic case and this for the non-linear displacements, phases and forces. The multi-objective optimization step consists in seeking the first Pareto front of several linear and nonlinear objective functions by using a genetic algorithm of type “NSGA” (Non-dominated Sorting Genetic Algorithm). The design parameters are: mass, linear and non-linear stiffness and damping of the absorber. To obtain solutions presenting a good compromise between optimality and the robustness, one introduces uncertainties on these design parameters. The robustness is then defined by the dispersion of the parameters (definite as the ratio: mean value/standard deviation) and it is introduced as additional objective function. The use of the clusters resulting from the Self-Organizing Maps of Kohonen (SOM) is also suggested for a rational management of the design space. A study of sensitivity a posteriori can be exploited in order to eliminate the non- significant design parameters. [1]