Analysis of energy conversion in two-mode vibration control using synchronized switch damping approach

The synchronized switch damping (SSD) approaches based on piezoelectric actuators have been successfully used in multimode vibration control of structures. By suppressing voltage inversion at some displacement extrema, the control performance of SSD approaches can be significantly improved. In this study, conversion of energy from mechanical to electrical in two-mode control is analyzed for different amplitude ratios and frequency ratios. The results show that the converted energy in two-mode control with voltage inversion at every extremum is smaller than the sum of the energies of the two modes in single-mode control, but the converted energy of the second mode in two-mode control may exceed that in single-mode control when the amplitude ratio of the second mode to the first mode is small enough. The influence of voltage threshold used to suppress voltage inversion on energy conversion of the system and each individual mode is also investigated. The converted energy of the first mode in two-mode control may be much larger than that in single-mode control when voltage inversion is suppressed suitably. The analytical results can successfully explain the phenomenon in the previous control experiments and can also be extended to multimode control.