Theoretical Upper and Lower Bounds of the Performance of an On-Off Damping Dynamic Vibration Absorber Attached to a Multi-Degree-of-Freedom System

Abstract

This paper reveals the theoretical (upper and lower) bounds of the performance of an on-off damping vibration absorber attached to an undamped multi-degrees-of-freedom (MDOF) system under harmonic excitation. The solution reduces to the maximization or minimization problem of a simple single-variable function. Among the class of on-off damping controller, which switches the damping level from high to low and back at fixed times every half period, the revealed solutions produce the highest and lowest amplitude–frequency curves. These curves are the good theoretical benchmarks to measure how good or bad an on-off damping controller is. To demonstrate the usefulness of the theoretical bound solutions, two versions of power flow-driven controller are introduced to produce the amplitude–frequency curves tracing the lowest-amplitude curve. A case study of a four-mass system is discussed.

Amplification of useful vibration using on-off damping

“…The same proof can be done as above when we observe (10) and (18). From (10), when zl=0 and zh tends to infinity, two terms zt and zs also tend to infinity. The expression (18) reduces to: It is seen that the useful vibration tends to the maximum one of the passive case in a wider range of frequency.…”

“…The expression (18) reduces to: It is seen that the useful vibration tends to the maximum one of the passive case in a wider range of frequency. The same proof can be done as above when we observe (10) and (18). From (10), when ζ l = 0 and ζ h tends to infinity, two terms ζ t and ζ s also tend to infinity.…”

“…In the field of vibration control, some papers pointed out how much useless vibration can be suppressed by a general controller of on-off damping [9][10][11][12]. In this paper, in the converse way, we derive clearly how much useful vibration can be extracted using on-off electrical damping.…”

Vibration suppression investigation and parametric design of tri-axle straight heavy truck with pitch-resistant hydraulically interconnected suspension

“…Recently, number of research efforts focused on the design and control to improve passive/active safety (Zhang et al, 2020). For instance, Viet and My (2019) revealed the performance limit of system with on-off damping absorber. Sakong et al (2020) investigated the isolation performances of the hydraulic system with modal analysis method.…”

“…Howerver, the pneumatic system is generally designed to generate the total suspension strut force (Shin et al, 2010), and hence it is more complex and requires higher maintenance cost in practice (Lu et al, 2018). The viscous damper used in the HIS system has many advantages, such as greater force output, more reliable work and easier for reverse control (Toyouchi et al, 2021). Furthermore, Smith and Walker (2005) stated that passive IS system can independently adjust damping/stiffness rates for specific vibration mode.…”