Vibration analysis of moving anisotropic thin plate, wrapped in translation process

Abstract

Natural vibration analyses of moving anisotropic plates under tension in helically translation process, considering the effect of stiffness, caused by tension and curvature in both stationary and moving manners, are presented. The paper aims to investigate conflicts between fiber orientation and geometrical asymmetry due to helical wrapping and translation dynamics on modal properties of moving narrow thin plates. Owing to the low bending rigidity, the plate is continuously wrapped around the roller, and it is assumed that the structure is composed of three flat–curved–flat segments. The governing equations of motion are extracted by the virtual displacement method and based on the Kirchhoff–Love’s plate–shell theory. In order to achieve the eigenvalue set, the Rayleigh–Ritz method is used together with the orthogonal approximation functions. Convergence of the method is also discussed, which shows an acceptable accuracy for less computational costs, compared to the finite element solution. Effects of the fiber orientation and velocity on the natural frequencies are also studied. On account of discrepancy between fiber and helix angles, different modal results are reported for two sides of the plate which are wrapped around the roller. Moreover, mode shapes are illustrated, and contributions of longitudinal and lateral directions are highlighted.