Frequency Analysis of Wing–Rotor System Considering Flexibility in Capsule Based on High-Accurate Method

Based on a typical wing–rotor thrust model on the airship, the dynamic influence of the gyroscopic effects from the tip rotor acting on the overall coupled system has been analyzed. Meanwhile, the flexibility at the capsule boundary has been studied, as well. Hamilton’s principle is employed to derive the general governing equations and the numerical Rayleigh–Ritz method is finally chosen in actual frequency computations. A new set of shape functions are put forward and verified which take most of the couplings among dimensions into account. The parameter studies are also conducted to make deep investigations. The results demonstrate that the inherent frequencies are significantly affected by the rotor speed and the flexible capsule condition. When rotor revolves, the modal shapes have reached into complex states and the components of each mode will change with the increment of rotor speed. The flexibility will also greatly reduce the entire frequencies compared with the rigid case. It is also demonstrated that the inherent property will be significantly affected by the mounting geometry, rotor inertia, the structural stiffness, and rotor speed.