Steady state response analysis for a switched stiffness vibration control system based on vibration energy conversion

A novel semi-active vibration control concept with a serial-switch-stiffness-system was previously presented in our work. Differing from conventional vibration control systems, this system does not dissipate but converts vibration energy as potential energy stored in springs and then reacts against external disturbance. As a piecewise linear system, whether or not energy conversion limit happens is an interesting nonlinear dynamic issue related to the systems steady state response. This paper formulates this issue in depth using the approach called equivalence in control. The systems control force represented by the converted vibration energy is approximately decomposed into two portions. One is responsible for low-frequency free response and the other for high-frequency switching response. An equivalent linear system suffering from a decomposed high-frequency switching force is obtained instead of the original switched system. The steady state response of the disturbed system can be delivered through linear superposition as executed in a linear system. Energy conversion limit occurring in the system under a harmonic disturbance is numerically shown by means of fast Fourier transformation. Analytical formulation and numerical simulation for open- and closed-loop control of the system are further carried out, respectively. The results give that the proposed approach is capable of solving the stead state response of the switched system accurately, and meanwhile, energy conversion limit occurs in the vibration control system indeed. Experimental discussion is also executed.

Automated summary

The study introduces a novel semi-active vibration control concept that converts vibration energy to potential energy stored in springs. By decomposing the control force into two components and using an equivalent linear system, the study accurately addresses the vibration control issue in steady state response and demonstrates the occurrence of energy conversion limit in the vibration control system.