Abstract
The optimal design of damping parameters for passive vibration control remains a challenge for both research and industrial applications. Here, we introduce a design methodology based on limit cycle analysis in concert with design optimization. A state-space representation is used to model the vibrational behavior converged to its limit cycle. The design approach is outlined and applied to mechanical systems undergoing periodic forces. This method is applicable to both vibration mitigation and energy harvesting, and examples of both are shown. We conclude with a summary of the results and an outlook for future developments and applications.