Continuum Modeling and Vibration Analysis of Cable-Harnessed Plate Structures of Periodic Patterns

Abstract

Over the past decade, modeling of cable-harnessed space structures has received special attention due to the need for better accuracies than the existing models. As these structures become more lightweight upon the advancements in the materials science it is imperative to further consider accurate models in which the dynamic effects of the added cables are better accounted for. Researchers have heavily focused on creating models for cable-harnessed beam-like structures, while very few works have considered plate-like structures. The proposed research aims at the development of an analytical model for cable-harnessed plate-like structures. Cables are assumed to be periodic in geometry to allow for the application of an energy-equivalent homogenization technique. To begin with, a linear displacement field and a second-order Green-Lagrange strain tensor for strain-displacement relationships are considered. The strain and kinetic energies of the fundamental element are found using these relations. The repeated pattern of the fundamental element over the area of the plate structure allows for the employment of the homogenization approach in which the kinetic and strain energies per area of the fundamental element are found and assumed to remain the same as an equivalent homogenized solid plate-like element. The governing dynamic Partial Differential Equations (PDEs) are found using the Hamilton’s principle. The results are validated using finite element analysis. A detailed parametric analysis is also performed to investigate the effects of various cable parameters and wrapping patterns on the dynamics of the host structure.