Optimizing natural frequencies in compliant mechanisms through geometric scaling

This work contributes to the dynamic analysis and optimization of compliant mechanisms in terms of their natural frequencies. The previously established analytical method based on Bernoulli beams and the transfer matrix method, which underlies the existing calculation tool CaTEf, is extended to enable the scaling of any specified geometric parameter or parameter set within a given mechanism to achieve a desired natural frequency. By introducing a scaling parameter, precise adjustments of selected geometric parameters are ensured while accounting for inherent dependencies. Minor discrepancies are revealed in parameter studies when comparing results obtained with our proposed analytical method to those from the Finite Element Method (FEM) regarding the resulting scaled values. Following validation, the analytical method is seamlessly integrated into CaTEf and verified against experimental data, demonstrating strong agreement. This work results in a highly efficient analytical method for optimizing compliant mechanisms in terms of their dynamic behavior, especially natural frequencies, while significantly reducing modeling and calculation time.