Modal and SEA Parameters of Ribbed Plates: master thesis

When predicting the vibrational behavior of structures several different approaches can be used. One approach is to use differential analysis and the wave equation. This however, can be rather cumbersome and computationally demanding. Another approach is to consider the modal density and the statistical distribution of energies in the structure. This latter approach will be the main topic of the present thesis. Rib reinforced plates are often used in lightweight building structures, vehicles, ships, aircrafts and so forth. In lightweight building elements the materials may be different kinds of wood, or perhaps wooden plates on steel frames, whereas constructions like vehicles, ships and aircrafts would more likely be made from some kind of metal or fiber material. What these otherwise different structures have in common, is that the reinforcing ribs are very often periodically spaced. Existing simplified prediction tools, such as Statistical Energy Analysis (SEA) are not always suitable for these kinds of constructions, as for instance standard SEA is based on diffuse field assumptions, which do not apply to rib reinforced plates. In order to adapt SEA theory to spatially periodic structures, the modal density of such structures need to be investigated. It the present thesis a modalmodel of a rib reinforced plate is presented and the modal density is investigated. The model is introduced by Chung [3] and is based on Hamilton’s Principle by considering the kinetic and elastic potential energies in bending plates and beams. The model, which is made ready for parallel computing, is implemented in MATLAB. It is shown that the modes of a spatially periodic ribbed plate can be divided into two groups; one showing periodic behavior in terms of pass bands and stop bands, and another that does not show such behavior. It is demonstrated that the rotational mass moment of inertia and the rotational stiffness are important to the pass band/stop band behavior. Further, simulations showing that the frequencies of the pass bands are determined primarily by the distance between the beams are performed. The period of the modal density of the perpendicular modes is seen to be proportional to kl. The hope is that the implemented model and the findings regarding the grouping of modes may help the process of developing an SEA based prediction tool for spatially periodic constructions.