The Properties of Structures with Two Planes of Symmetry

In the domain of civil engineering, the structures encountered usually present symmetries of different types. The causes that determine the use of these symmetries are diverse, starting from esthetic motivations but also dictated by practical reasons, such as the reduction in construction time and costs. These geometric symmetries lead to specific properties that, in certain situations, can help to simplify the calculation of these structures. They can be identified both in the static analysis and the deformability of the structure, as well as in the dynamic analysis in the study of vibrations. If these properties are used, it is possible to reduce the analysis time, and the designer can obtain a quick estimate of the behavior of the structure. Starting from these considerations, this work will determine some of the properties specific to the natural vibrations of certain structures with identical parts in their components (structures that present two planes of symmetry) and will demonstrate how these properties can contribute to reducing the time required for dynamic analysis. An example will be used to exemplify the presented methods. This work allows for further developments and makes possible the development of the existing finite element software by adding some modules to identify such situations by analyzing the input data and using the properties described in the newly introduced algorithms.