Numerical investigation of natural frequencies and mode shapes of air-supported structures

Natural frequencies and mode shapes are important properties of engineering structures and buildings. Modal analysis of the prestressed membrane structures made of orthotropic material is described in this paper. The equation of motion of the system with finite number of degrees of freedom was given in the matrix form. Features of the modal analysis of prestressed system are described. To validate our technique, we have found in the literature and repeated the modal analysis of cylindrical membrane structure (inflated beam). In the source paper the analytical solutions for the natural frequencies were obtained for the one-dimensional (beam) model with taking into account orthotropic mechanical properties and prestress. In this paper the test case was solved for the spatial shell model using finite element analysis, realized in program software “ANSYS Mechanical”. Comparison between authors’ results and results described in reference is carried out. The possible reasons of results divergence are explained. The validated technique has been applied to modal analysis of an air-supported structure based on the rectangular plan of 20×50 m. Models with different mesh sizes were used to achieve the mesh convergence of results. Almost linear dependence between internal pressure and squares of natural frequencies has been received. This result is in the accordance with known solutions, described in the literature for isotropic membranes.