Convergence in Modal Synthesis

To accurately determine all of a system’s vibration modes with a frequency less than some frequency Ω, frequency those component modes with natural frequencies less than Ω or in the mathematical neighborhood of Ω need be included in the system equation-of-motion. The process of selecting component modes as generalized coordinates in a system equation of motion requires some knowledge of how these modes will contribute to the system solution. A development showing how the component eigenvalues can be used to establish bounds on the eigenvalues of the system is presented along with two convergence criteria for the system frequencies based on the component frequencies. Some numerical results show that these developments can help a user of this method minimize problem size and costs without sacrificing accuracy.