Introduction and Optimization of a Novel Nonlinear Model for the Free Vibration of Warp-knitted Spacer Fabrics

The aim of this study is to present a nonlinear model that can describe the free vibration damping behavior of 3D knitted fabrics. A fabric is considered as a single degree of freedom model which consists of a nonlinear spring paralleled with a dashpot both in series with a mass. The differential equations of the system motion are solved using the multiple scales method. Damped frequency ω_d and damping coefficient $\hat{\mu }$ are determined using the approximate analytical method, the Imperialistic Competitive Algorithm (ICA) and linear methods to estimate the system response. The obtained system response is then compared with experimental results. The results of the study show that, in comparison with analytical solutions and linear models, ICA can predict the behavior of spacer fabrics more accurately. It is also found that the difference between experimental and predicted models is explained by errors of 8.3 %, 13.7 % and 16.2 % for ICA, approximate analytical and linear model respectively.