Vibrations Analysis of Cable-Harnessed Plates: Continuum Modeling and Experimental Validation

Dynamic modeling of spacecraft structures is imperative to their successful design for flight missions. A large number of these structures' dry mass consists of signal and power cables, dynamics of which is not well-predicted using ad hoc cable lumped mass models. Hence, accurate modeling techniques are required to understand these cable dynamics effects. In the past, efforts toward developing analytical models for cable-harnessed structures have been primarily focused on beam-like host structures. The presented paper is aimed to fill this gap by obtaining analytical solutions through an energy-equivalent homogenization approach for cable-harnessed plate-like structures and to ultimately help with understanding the dynamic effects of signal and power cables on two-dimensional plate-like structures. As a first step, systems of periodic geometries with parallel cable configurations are considered. The strain and kinetic energy expressions for the fundamental repeated elements are found using linear displacement fields and Green-Lagrange strain tensors. The governing partial differential equation (PDE) for the out-of-plane motion of the cable-harnessed system is then found using Hamilton's principle. Experimental modal testing is performed for the purpose of validations of the frequency response functions (FRFs) obtained from the model for the cable-harnessed plates under clamped-free-free-free boundary conditions. The results clearly show the dynamic effects of the (CFFF) cables which are also well-predicted by the model. Finally, modal assurance criterion (MAC) analysis has been used for further validations of the mode shapes obtained from the model.