Statistical response of a simplified nonlinear fluid model under random parameters

In this paper, a simplified spring-dashpot model is proposed to represent the complicated nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been adopted by many researchers to characterize some parts of human body in bioengineering. Among others, the following researchers have already contributed to the development of this field (Weiss et al., [1]; Guedes et al., [2]). Sometimes it is impossible to estimate the constant parameters in the model deterministically, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to characterize the random properties of the viscoelastic materials. The mean value of the displacement of the nonlinear model, subjected to constant rate displacement, can be solved analytically. Based on the closed-form solution, the proposed method produces the statistical responses of the simplified nonlinear fluid model, which is fairly useful in estimating the reliability of the nonlinear system.