Multi-supported beam structures are widely used in engineering applications, particularly as sensitive components in resonators. The intrinsic properties of these sensitive components significantly influence the performance of resonators. In this study, a dynamic theoretical model of a multi-point supported beam was established, considering the impact of the supported beams on the overall structure. The governing equations of motion of the multi-point supported beam structure were derived using the Hamiltonian principle. A theoretical method was proposed to calculate frequencies and global modal shapes of the multi-point supported beam structures. The theoretical results were validated through numerical simulations with specific parameters. The natural frequencies of a multi-point supported beam were also experimentally measured and compared with the simulation results. Our investigation into the effects of structural parameters on the frequency and global modal shapes demonstrated the effectiveness of the proposed method. The findings show that frequencies and modal shapes of the complex beam undergo regular changes as structural parameters vary. This study provides a theoretical foundation for improving the performance of beam resonators and serves as a guide for the parametric design of multi-point supported beam structures.
