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Two damping rings (DRs) are added on a nonlinear free-free elastic beam to reduce vibrations. This elastic beam with free-free boundary conditions can be used to simulate the high speed aircraft fuselage vibrations. Both isotropic beam and compound beam with double-section are investigated. The beam is subjected to a distributed load with the harmonic wind force. The method of multiple scales ((MOMS) a perturbation technique) is employed to analyze this nonlinear problem in frequency domain. DRs with various locations, masses, spring constants, and damping coefficients are analyzed and the maximum amplitude counter plots (MACPs) are compiled to identify DRs’ combinations for the optimal damping effects. The Floquet theory is used to make the basin of attraction (BOA) charts and analyze the stability of the system. This research can be applied in a wide range of engineering problems, such as rocket structures, high-speed aircrafts, satellites, missiles, etc.