Sequential design of two orthogonal dynamic vibration absorbers in a pendulum based on stability maximization

Abstract

A dynamic vibration absorber moving in the tangential or in the normal direction of a pendulum's orbit can reduce the free vibration of the pendulum. This article discusses the problem of a pendulum structure attached with two dynamic vibration absorbers moving orthogonally at the same time. The analytical optimization is proposed to be done in two steps, in which the parameters of the linear dynamic vibration absorber moving in tangential direction and the non-linear dynamic vibration absorber moving in normal direction are chosen sequentially based on the stability maximization criterion. The analytical analysis shows that the two-dynamic vibration absorber scheme has small benefit in comparison with the single-dynamic vibration absorber scheme. The analytical conclusions are verified by numerical calculations. Although the conclusion of the article is unexpected, it is important in practice because the two-dynamic vibration absorber arrangement can be excluded in the design.

A single mass dynamic vibration absorber producing linear damping, Coriolis damping and gyro-damping

“…The DVA's parameters are determined such that the system has four poles with the same real parts and the same absolute values of the imaginary parts. The detailed procedure has been presented in (7) and the analytical forms of the optimal parameters are summarized in Table 4. -Case 3: The DVA has only normal translation z u .…”

“…In the combined DVA, the stiffness' mistuning is considered in the worst case, in which the component stiffnesses k v , k u , and k g simultaneously have the same mistunings. To emphasize the influence of the nonlinearity, let us return to the fourth equation of (7). We see that the nonlinearity increases due to two external sources: the pendulum angle and the rotor speed .…”

“…However, in a pendulum, a DVA placed at the location of large motion such as gravitational center of pendulum works poorly. 5–8 This surprised result led other researchers to incorrectly conclude that it was impossible to reduce vibration of pendulum-type structures using DVA. In our point of view, that is the possible reason why there is still limited report on the problem of using DVA in a pendulum.…”

A global-local approach to the design of dynamic vibration absorber for damped inverted pendulum structures

“…is introduced for a local domain Φ with 0 ≤ Φ ≤ 2π. The criterion (20) leads to dS/dγ = 0. Thus, we have…”

“…Viet et al [18] investigated a DVA moving in the normal direction by using the effective damping approach. Viet et al [19,20] studied a DVA moving in both tangential and normal directions and two orthogonal DVAs for conventional pendulum structures.…”