Response of linear or complex nonlinear structures takes form in a characteristic functions and in the deterministic or stochastic external loads. Non linear model with non linear structure stiffness is a type of Duffing equation. Stochastic external loads system is referred to a random signal white noise with a constant power spectral density (So), while non linear system identification of deterministic system's is based on time history, phase plane and Poincare map. Methods of Galerkin and

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... ge-Kutta are used to solve the partial non linear governing diferential equations. Mean value , Standard deviation and Probability Density Function (PDF) is stated as statistical responses due to stochastic response of random variables. The analysis of random vibration in the solution of non linear stochastic differential equation is solved