Introduction and Optimization of a Novel Nonlinear Model for the Free Vibration of Warp-knitted Spacer Fabrics
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ISSN 1229-9197 (print version) ISSN 1875-0052 (electronic version)
Introduction and Optimization of a Novel Nonlinear Model for the Free Vibration of Warp-knitted Spacer Fabrics M. Taghvaie1, P. Payvandy1*, and M.M. Jalili2 1
Department of Textile Engineering, Yazd University, Yazd 89195-741, Iran Department of Mechanical Engineering, Yazd University, Yazd 89195-741, Iran (Received July 21, 2019; Accepted December 15, 2019)
2
Abstract: 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 ωd and damping coefficient µˆ 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. Keywords: Spacer fabric, Nonlinear vibration, Nonlinear stiffness, Method of multiple scales
of warp-knitted fabrics made for cushioning applications. Their result showed that warp-knitted spacer fabrics are an ideal category of energy absorbers for cushioning applications. It was also revealed that fabrics with a larger spacer yarn inclination angle, less thickness, coarser spacer yarns, and smaller mesh size of the outer layers can absorb higher energy with higher efficiency. In 2015, Du et al. [23] studied the pressure relief property of spacer fabrics. Their results pointed to improved pressure concentration and decreased pressure peaks in those fabrics. They also indicated that seated volunteers’ weight can influence the contact area, average pressure and average gradient integral. Some researchers have also investigated the behavior of spacer fabrics in the absorption of compression energy by plane and spherical compression surfaces. In 2012, Du and Hu [24] developed a theoretical model to predict the compression behavior of spacer fabric in spherical form. It was found that the spherical compression force and strain decrease as the radius of a ball increases, and they increase as the fabric thickness increases. In a subsequent study in 2012, Du and Hu [25] conducted experimental measurements on the model developed in their previous work and compared the results. Du et al. [26] in 2017 investigated the spherical compression behavior of warp-knitted spacer fabrics. The displacements and the stress distribution of spacer filaments under compression forces were also analyzed to understand the me
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