Natural frequency extraction of a beam-moving mass system with periodic passages using its pseudo-natural frequencies

Wind turbines, helicopters, and turbo-machineries' rotary motion, along with a variety of nonlinear structures linearized with their periodic limit cycles, may all contain time-periodic terms in their equations of motion even if the equations remain linear. The purpose of this study is to model these systems into a beam-moving mass system. Natural frequencies of the beam are calculated using past work in which pseudo-natural frequencies of a beam-moving mass system were extracted, followed by the homotopy perturbation method. The findings of this study are valuable to the industry, and they decrease error margin in resonance range assessment. This approach indicates that for beam-moving mass systems, extraction of natural frequencies that ignore the moving mass effect can lead to inaccurate results, whereas only a limited amount of physical data are needed obtain accurate calculations. Furthermore, this study used homotopy perturbation for operational modal analysis purposes and not for solving nonlinear equations.