Extensional damping

Their arrangement in space is illustrated in Figure 14. An extensional damping... 

Broadly speaking, extensional damping utilizes E while constrained layer... 

The two methods are compared in Table I. While extensional damping is clearly... 

Figure 8. Design of a barbell test assembly used to evaluate the extensional damping performance of constrained-layer treatments.

Figure 9. Calculated vs. measured extensional damping performance for the Figure 8 test assembly.

The empirical temperature bandwidth constant (K), a measure of extensional damping effectiveness, is strongly affected by polymer secondary loss mechanisms. Polymers such as PMMA and PEMA form very effective damping materials because they possess broad temperature span lossy modulus curves. 

The damping terms follow from basic viscoelastic behavior (see Chapter 2). Extensional damping follows the loss modulus, E". On the other... 

Extensional damping, where a polymer is placed as a free layer on the resonating vibrating system and... 

In the same way, but much more complicated, with a damping function depending on the Hencky strain, it proved to be possible to calculate the transient extensional viscosity as a function of qe. The result is illustrated in Fig. 15.30 for the same polymer. It shows that extensional viscosity remains finite and increases with increasing strain rate up to a maximum at qe = 2 s, after which it decreases again. The calculated lines coincide quite well with the experiments, but the calculated viscosities are somewhat too high. 

Table I. Comparison of Extensional and Constrained Layer Damping...

Figure 7. Constrained-layer damping of extensional and flexural vibrations of bars and plates.

Two widely applied damping configurations that use viscoelastic materials are the free viscoelastic layer and the constrained viscoelastic layer, as shown in Fig.9a and 9b. The deformation of the viscoelastic layer is extensional in the first case and shear in the second case. Both these deformations are highly damped by intrinsic absorption in the viscoelastic polymer. In the case of the free viscoelastic layer (Fig.9a) it flexes with the plate participating in the bending stiffness as part of a two-layer beam. The viscoelastic layer must be tightly bonded to the plate and must be continuous over a... 

Incidentally, Kerwin and Smith (2il) have shown that essentially the same segment-length optimization yields best damping of longitudinal or extensional waves in the base plate. The segmented constrained viscoelastic layer is one of the few treatments capable of providing useful damping of such waves, which are troublesome in certain cases. 

Sound and vibration damping research with IPNs began in the early 1970 s and resulted in the formation of a constrained layer damping system with the inner damping layer a latex IPN paint (3 ). The constrained layer system results in a shearing effect within the IPN layer along with flexural and extensional motions as the composite panel vibrates. The added shear mechanism, not present in extensional applications, increases the amount of energy that is dissipated in each vibrational cycle. 

A few rheometers are available for measurement of equi-biaxial and planar extensional properties polymer melts [62,65,66]. The additional experimental challenges associated with these more complicated flows often preclude their use. In practice, these melt rheological properties are often first estimated from decomposing a shear flow curve into a relaxation spectrum and predicting the properties with a constitutive model appropriate for the extensional flow [54-57]. Predictions may be improved at higher strains with damping factors estimated from either a simple shear or uniaxial extensional flow. The limiting tensile strain or stress at the melt break point are not well predicted by this simple approach. 

Two types of damping configuration are in common use. Application of a single layer of polymer on the vibrating surface is called extensional... 

The vorticity diffusion in a-vortex attached to the wall in a complex eigenvalue critical point is investigated. It is shown that extensional viscosity is produced near the critical point. The internal strainfield of the vortex rods is damped and an accelerated vorticity diffusion occurs due to polymer additives. 

Figure 8.6 ° demonstrates the damping capabilities of formula G in both extensional and constrained layer modes as a function of temperature. In the latter mode, a constraining layer material based on reinforced epoxy resin was used. 

Figure 8.6. Extensional and constrained layer damping of formula G as a function of temperature. ...

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