Natural Frequencies of Composite Anisogrid Cylindrical Shell-Beams Carrying Rigid Bodies at the Boundaries: Smeared Approach, FEM Verification, and Minimum Mass Design

In this paper, the natural frequencies of pure bending, axial–bending, and torsional-bending coupled modes of CFRP Anisogrid cylindrical shell-beams supporting non-structural masses and inertias at the boundaries are firstly analytically investigated and, secondly, verified by FEM. Indeed, the design of shell-beam elements in various engineering applications is driven by the minimum frequency value that is necessary to achieve in order not to compromise the proper functionality of the assembly for which these elements are designed. In turn, this minimum frequency depends on the geometry, mass, and dynamics of the main components of the assembly. A typical point in space applications is to control the lowest frequency of the spacecraft body, commonly supported by a shell structure, in order to avoid the occurrence of resonance issues that may be induced by dynamic loads during the launch phase. As a rule, to keep the lowest frequency sufficiently high, in conjunction with non-structural masses, means to increase the stiffness and the mass of the load-carrying structure and, ideally, to identify the most efficient solution. In order to effectively address this topic, the analytical models of the natural frequencies of Anisogrid cylindrical shell-beams are finally introduced into an optimization routine as constraints on the fundamental frequency. This approach allows us to readily explore the various Anisogrid configurations and find the best candidate solutions in the framework of preliminary design.