Dynamic response of geometrically nonlinear, elastic rectangular plates under a moving mass loading by inclusion of all inertial components. (28th April 2017)

• Record Type: Journal Article
• Authors: Rofooei, Fayaz R.; Enshaeian, Alireza; Nikkhoo, Ali
• Is Part Of: Journal of sound and vibration. Volume 394(2017)
• Page Start: 497
• Page End: 514
• Publication Date: 2017-04-28
• Subjects: Von Karman rectangular plate -- Moving mass -- Geometric nonlinearity -- Finite element method; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2017.01.033
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: Dynamic deformations of beams and plates under moving objects have extensively been studied in the past. In this work, the dynamic response of geometrically nonlinear rectangular elastic plates subjected to moving mass loading is numerically investigated. A rectangular von Karman plate with various boundary conditions is modeled using specifically developed geometrically nonlinear plate elements. In the available finite element (FE) codes the only way to distinguish between moving masses from moving loads is to model the moving mass as a separate entity. However, these procedures still do not guarantee the inclusion of all inertial effects associated with the moving mass. In a prepared finite element code, the plate elements are developed using the conventional nonlinear methods, i.e., Total Lagrangian technique, but all inertial components associated with the travelling mass are taken into account. Since inertial components affect the mass, damping, and stiffness matrices of the system as the moving mass traverses the plate, appropriate time increments shall be selected to avoid numerical instability. The dynamic response of the plate induced by the moving mass is evaluated and compared to previous studies. Also, unlike the existing FE programs, the different inertial components of the normal contact force between the moving mass and the plate are computed separately to substantiate the no-separation assumption made for the moving mass. Also, it is observed that for large moving mass velocities, the peak plate deformation occurs somewhere away from the plate center point. Under the two extreme in-plane boundary conditions considered in this study, it is shown that if the geometrical nonlinearity of plate is accounted for, the deformations obtained would be less than the case with classical linear plate theory. Highlights: All inertial components of the moving mass are included. Dynamic results of linear plates envelope those of geometrically nonlinear plates. Plate's peak deflection shifts away from the center point for fast moving masses. Plate's in-plane boundary conditions affect results only if nonlinearity is included. Spectral radius of the incremental dynamic equations should be observed in selecting the integration time steps.