Frequency optimization with respect to lumped mass position

The sensitivity analysis of a natural frequency with respect to the change of a lumped mass position has been a research topic for some time. However, relatively little work has been done on optimizing the lumped mass position. The frequency sensitivity with respect to both the position and magnitude of a lumped mass is investigated by the discrete method. Furthermore, an evolutionary algorithm is presented for frequency optimization of beam and plate structures to positions of the lumped mass attachments, which can move in the structural domain. Based on the design sensitivity analysis, the most efficient lumped mass is shifted to optimize the frequencies asymptotically. Three model examples are provided to demonstrate the validity of the sensitivity analysis and the effectiveness of the optimization method.