Eigenvalue formulation for antiresonant and extremum response frequencies under harmonic base excitation

Eigenvalue formulation methods for determining the frequencies of antiresonance and local extrema in the frequency response have been shown to be successful in the numerical simulation for undamped structures under force excitation. In aerospace engineering, however, base-excited vibrations during launch and flight pose critical threats to sensitive components, demanding accurate prediction of these frequencies to guide structural optimization and modification for targeted vibration suppression. To address this, we extend our previous eigenvalue formulation method to include harmonic base excitation in this paper, making it more versatile. As demonstrated in the orbital module case study, this extension enables accurate frequencies prediction for large-scale complex spacecraft under base excitation scenarios. Furthermore, a comprehensive theoretical explanation of why the structural natural frequencies appear in various eigenvalue formulation methods for determining antiresonant frequencies is provided, addressing a previously unexplained aspect of this methodology. To demonstrate the proposed method, besides the numerical application, vibration experiment for a cantilever beam with base excitation was also carried out. The test results confirm the theoretically predicted antiresonant and extremum response frequencies. The test results also support the validity of undamped assumption for structures with light damping.