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1.3.1.2 Dynamic Vibration Absorber

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The harmonic oscillator can be an anti-vibration device. This is called a tuned vibration absorber (TVA) or dynamic vibration absorber (DVA) and is a kind of multi-purpose tool whenever you have to combat resonance issues. It is a very useful device if vibration at a particular frequency must be reduced. Many applications are single frequency cases as for example propeller harmonics. In addition DVAs are used for reducing the resonance effects under broadband excitation. Usually real technical systems have multiple resonances but the principle can be shown with a SDOF system as master system. In Figure 1.14 such a setup is shown. The exciting force can be for example a rotating or vibrating machinery.


Figure 1.14 DVA mounted on resonant master system. Source: Alexander Peiffer.

The equation of motion is

(1.84)

with the following transfer function

(1.85)

The result is non-dimensionalized by dividing through the static response u1(0)=Fx1/ksb.

Assuming zero damping gives the characteristic equation for the combined resonances

(1.86)

With the resonance frequencies of each single system ω02=ksb/m, ωs2=ks/ms and the mass ratio μ=ms/m the resonance frequencies of the combined undamped system are given by

(1.87)

Figure 1.15 shows the result for a master system with m = 0.1 kg and ksb=10 N/m and an additional DVA tuned to the same frequency as the master system with ms=0.02 kg and ks=2 N/m. Several curves for different critical damping ζ are given. From the undamped case we learn that the response can theoretically be reduced to zero but implicating two resonances at different frequencies. With additional damping the response can be diminished for a broad frequency range. The design of the best DVA is an optimisation task depending on several constraints as discussed in detail by Harris and Crede (1976). In the optimisation procedures issues such as total mass, DVA mass displacement, linearity range of the spring, and the dynamic must be considered.


Figure 1.15 1DOF system with and without DVA. m = 0.1 kg, ms=0.02 kg, ksb=10 N/m, ks=2 N/m. Source: Alexander Peiffer.


Figure 1.16 Frequency spread for DVA tuned to the same frequency depending on mass ratio. Source: Alexander Peiffer.

Vibroacoustic Simulation

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