Nonlinearities and high-order effects on membranes vibration

The design of membrane structures for aerospace applications, such as solar sails, antenna reflectors, and habitat modules, has gained significant popularity due to their thinness and inflatable or deployable nature. These structures are convenient to stow in a launcher, taking up minimal space, and once deployed in orbit, they provide a large volume with a very low weight/volume ratio. To ensure the successful design and deployment of the structure, accurate structural analyses are necessary, including modal analysis, to understand how the membrane will respond to vibrations. Despite the task's difficulty, due to the nonlinearity of geometrical deformation, initial stress, and air-elastic effects, determining the natural frequencies and mode shapes is essential for proper verification and analysis of the structure. This work presents the results of modal analyses conducted on a membrane solar panel. The methodology is based on the Carrera Unified Formulation (CUF), which exploits generalized kinematics that applies an arbitrary expansion to the generalized variables. The structures have been analyzed using a low-thickness plate model, and the results have been compared by using commercial software tools. The investigation revealed that the bending stiffness of the plate structures influences the natural frequencies, and the system does not behave like an ideal membrane. Moreover, it was found that mode aberration phenomena occur and that increasing the pretension applied nonlinear effects exists. Furthermore, the impact of the theory approximation order along with the thickness ratio was evaluated.