On the Attachment Location of Dynamic Vibration Absorbers

Abstract

In mechanical engineering a commonly used approach to attenuate vibration amplitudes in resonant conditions is the attachment of a dynamic vibration absorber. The optimal parameters for this damped spring-mass system are well known for single-degree-of-freedom undamped main systems (Den Hartog, J. P., 1956, Mechanical Vibrations, McGraw-Hill, New York). An important parameter when designing absorbers for multi-degree-of-freedom systems is the location of the absorber, i.e., where to physically attach it. This parameter has a large influence on the possible vibration reduction. Often, however, antinodal locations of a single mode are a priori taken as best attachment locations. This single mode approach loses accuracy when dealing with a large absorber mass or systems with closely spaced eigenfrequencies. To analyze the influence of the neighboring modes, the effect the absorber has on the eigenfrequencies of the undamped main system is studied. Given the absorber mass, we determine the absorber locations that provide eigenfrequencies shifted as far as possible from the resonance frequency as this improves the vibration attenuation. It is shown that for increasing absorber mass, the new eigenfrequencies cannot shift further than the neighboring antiresonances due to interlacing properties. Since these antiresonances depend on the attachment location, an optimal location can be found. A procedure that yields the optimal absorber location is described. This procedure combines information about the eigenvector of the mode to be controlled with knowledge about the neighboring antiresonances. As the neighboring antiresonances are a representation of the activity of the neighboring modes, the proposed method extends the commonly used single mode approach to a multimode approach. It seems that in resonance, a high activity of the neighboring modes has a negative effect on the vibration reduction.

Active Dynamic Vibration Absorber for Broadband Control of a Multi-Mode System: Simulation and Experimental Verification

“…Also, the mode shape of the first floor, second floor and third floors for n-th mode is X n = [x n1 , x n2 , x n3 ] T . (10) is modified based on three different attachment points of the ADVA on the building model [17]. Since proportional damping is assumed for the system, the damping property of the building model is assumed negligible.…”

Beyond the Tuned Mass Damper: a Comparative Study of Passive Approaches to Vibration Absorption Through Antiresonance Assignment

“…The "single-mode approach" effectiveness decreases for systems with closely spaced natural frequencies and large absorber mass as demonstrated in [66] in the case of weakly coupled systems. In the light of this limitation, a great contribution is provided in [67], where the attachment location of the TMD is discussed by evaluating the shift in the eigenfrequencies of the modified system caused by the introduction of the TMD as sketched for a sample system in Fig. 14.…”

“…The development of the denominator in Eq. ( 19) through different approximations of (j ) explains the "single-mode approach" in term of spectral gap [67]. Under the approximation of (j ) through one mode, the characteristic polynomial is written as: Hence, fixed m a , the largest spectral gap from r,i is achieved for the maximum value of , (a) 2 .…”

“…Under the approximation of (j ) through one mode, the characteristic polynomial is written as: Hence, fixed m a , the largest spectral gap from r,i is achieved for the maximum value of , (a) 2 . If (j ) is represented through the contributions of all the modes, as in the "multi-mode approach" [67], the characteristic polynomial becomes:…”

Seismic vibration control of building structures with multiple tuned mass damper floors integrated

“…In general, the antinodal location of a single mode is taken as a priori for the attachment location [e.g., ]. However, this single mode approach loses accuracy for the cases of large mass TMD attached systems with closely spaced natural frequencies, while the multimode approach proposed in can solve these problems. Therefore, the multimode approach is applied to search the optimum TMD floor locations.…”