Design of semi-active dry friction dampers for steady-state vibration: sensitivity analysis and experimental studies

Abstract

Semi-active dry friction dampers with proper control strategies on the normal force can outperform the conventional passive frictional dampers. In this paper, a design approach based on global sensitivity analysis is proposed to determine the active normal force for the reduction of steady-state vibration. The unknown time-varying normal force is first expressed by a truncated Fourier series composed of several harmonics with respect to the excitation frequency. The Fourier amplitude sensitivity test (FAST) is then performed to identify the significance of each harmonic with regard to the overall damping. Only the most influential harmonics are kept in the following optimization process. This not only accelerates the design procedure but also simplifies the implementation of the active normal force. A single-degree-of-freedom (SDOF) system with a frictional contact to the ground is considered as an example to illustrate the proposed design approach. The multi-harmonic balance method (MHBM) is employed to calculate the required forced response results. Global sensitivity results indicate that only the second harmonic significantly impacts the damping performance. The results from sensitivity analysis are confirmed numerically and theoretically, leading to a relatively simple implementation. Compared to the optimal passive dry friction damper, the proposed design not only reduces the magnitude of the resonance peak, but also extends the useful range of excitation amplitude in which the system works. Finally an experimental study is carried out. Two cantilever beams are connected through a smart bolt, which can control the normal force applied to the joint with a piezoelectric actuator. Experimental results confirm that, with the appropriate phase condition, the second order harmonic improves the damping effect while the first order harmonic has nearly no effect. Furthermore, the phase condition to optimize the damping is close to the theoretical derivation except for a small delay. The phase range leading to better damping effect is relatively large. This experiment provides a feasible way to further increase the frictional damping of connecting structures. The proposed design approach is applicable for any dry friction damper capable of an active normal force.