Layer viscoelastic

Note that for autohesion of viscoelastic layers in contact above To, that the above equations can be utilized by substituting for I with the molecular structure factor H t) (and appropriate ratios) from Table 1 such that... 

These correspond, respectively, to polymer or electrolyte entrapped within surface features, the polymer film, and the solution. The first of these is a minor effect when using polished crystals the surface mechanical impedance of this contribution is Z, = wp where j = V-l, o> = 2nf0, and p is the areal mass density of the entrapped material. For finite and semiinfinite viscoelastic layers, the surface mechanical impedance is given by Z, = (GPf)m and Zv = (Gpf)1/2 tanh(y/i/), respectively, where prf and hf are the film density and thickness and y = /w(p/G)l/2. For the solution, Zs = (tapsT]J2)m (1 + j), where p, and tj, are the density and viscosity of the solution. When rigid mass, finite viscoelastic film and semi-infinite liquid loadings are all present, as in the experiment of Fig. 13.7, one can show that [42] ... 

This chapter discusses current research on the use of sulfur in recycled asphaltic concrete pavements. In addition, it describes the results of laboratory tests and theoretical predictions using the latest linear viscoelastic layered pavement analysis methods (15,16) to compare the performance of various sulfur-asphalt concrete pavements with conventional asphalt concrete pavements in a variety of climates. The relationship between pavement distress and performance used in the computer program was established at the AASHTO road test (17). Finally, the results of domestic field tests of sulfur-asphalt pavements are presented along with a discussion of future trends for the utilization of sulfur in the construction of highway pavement materials. 

Kanazawa et al. [20] and their calculations are valid for rigid films immersed in liquid. However, this work is not valid for non-rigid soft materials. For soft material layers it was even noticed that in applying Sauerbrey s equation the mass of the viscoelastic layer is underestimated and the result is a missing mass which was elucidated in calculations by Voinova et al. [21],... 

For each of these, displacement maxima occur at the crystal faces, making the device sensitive to surface perturbations. The perturbations to be considered in this section include surface loading by (1) an infinitesimally thick mass layer, (2) a contacting Newtonian fluid, and (3) a viscoelastic layer of finite thickness. 

Even though these transitions are different in many ways, as demonstrated below, the way in which acoustic energy interacts with polymeric materials permits us to use AW devices to probe changes in polymer film viscoelastic properties associated with these transitions. It should be emphasized up front, however, that evaluating the viscoelastic properties (e.g., modulus values) requires an ability to effectively model the film displacement profiles in the viscoelastic layer. As described in Section 3.1.8, the film displacement effects are dictated by the phase shift, , across the film. Since depends on film thickness, perturbations in acoustic wave properties due to changes in viscoelastic properties (e.g., during polymer transitions) do not typically depend simply on the intrinsic polymer properties. This can lead to erroneous predictions if the film... 

Admittance-vs-frequency measurements made at several temperatures on a polyisobutylene-coated TSM resonator were fit to the equivalent-circuit model of Sections 3.1.3 and 3.1.9 to determine values of G and G for the film [66]. These extracted values are shown in Figure 4.4, along with 5-MHz values obtained from the literature for polyisobutylene having an average molecular weight of 1.56 X 10 [44]. We note excellent agreement between the extracted and literature values of G from —20°C to 60°C, and in G" from —20°C to 10°C. Above 10°C, the extracted G" values are approximately 30% higher than the literature values. These results illustrate how AW devices can be used to quantitatively evaluate the viscoelastic properties of polymer films. Similar models for other AW devices, such as the model for SAW devices coated with viscoelastic layers (Section 3.2.7 and [61]), can enable these other devices also to be used to determine modulus values. However, the pure shear motion of the TSM does simplify the model, and the evaluation of the modulus values as compared with the more complex displacements of other AW devices such as the SAW device (a comparison of the models of Section 3.1.9 for the TSM and Section 3.2.7 for the SAW demonstrates this point). 

Fig. 5. Calculated structural loss factor based on RKU model for three-layer composite with varying Young s storage modulus and loss tangent of viscoelastic layer.

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... 

In contrast to the free layer, the operation of the constrained viscoelastic layer (Fig.9b) involves shear deformation of the layer [47]. Significant dampling can be achieved in the frequency range where there is a balance between the shear stiffness of the viscoelastic layer (2) and the extensional stiffness of the constraining layer (3). In this region the composite loss factor varies approximately as follows. 

Acoustic response of viscoelastic fluids may be simulated by Lagrangian finite element or Eulerian finite difference schemes. Both techniques have been used to predict the behaviour of discontinuous viscoelastic layers which may contain inserts such as air cavities and which are backed by metal plates. 

The Free Viscoelastic Layer. As we see in Figure 3, the free viscoelastic layer is bonded to the plate to be damped. As the plate vibrates in bending, the viscoelastic layer is deformed principally in extension and compression in planes parallel to the plate surface. Such damping layers have long been known, and at first were applied more-or-less empirically. In the early 1950s Oberst 3.,D and Lienard (, ) published analyses describing quantitative analytical models of free layer behavior. 

The damping performance of a free layer treatment for plate bending waves is shown in Figure 4 (lH,UL) This chart, which is Oberst s result, gives the system loss factor T relative to T 2/ the loss factor of the viscoelastic material, as a function of the thickness ratio H2/H1 (viscoelastic layer to plate). Each of the several curves corresponds to a particular value of the relative Young s storage modulus E2/E1 (viscoelastic layer to plate). 

Figure 3. Free and Constrained Viscoelastic-Layer Damping Treatments...

Layer (T 2 and T Loss Factors of Viscoelastic Layer and Composite) (Adapted from ref. 6)... 

The Constrained Viscoelastic Laver. The second of our two general damping treatments is the constrained viscoelastic layer shown in Figure 3(b). The complete constrained-layer configuration is a three-layer laminate comprising base layer to be damped, viscoelastic layer, and constraining... 

However, in the mid-frequency region, where the elastic energy in the viscoelastic layer can represent a useful fraction of the total, the system loss factor rises and passes through a maximum. Figure 5 shows this behavior with the wavelength X) dependence represented by a "shear parameter" y defined as follows ... 

Figure 6. Shear Relaxation in a Constrained Viscoelastic Layer Treatment...

The loss factor peak which occurs at Yopt can be located in frequency by the appropriate choice of the parameters that define y (see below). The maximum loss factor Tjmax the peak is governed by T 2 the loss factor of the viscoelastic layer and by a "stiffness" parameter Y simply defined as (17)... 

The Stlffness/Geometric parameter Y which defines the "severity" of the bending-wave dispersion characteristic between coupled and uncoupled conditions. Y and the loss factor T 2 of the viscoelastic layer determine the maximum system damping for the treatment. 

Variations on Constrained Viscoelastic Laver Systems. The constrained viscoelastic layer treatment. as applied to a base member, is at its simplest, a continuous 3-layer laminate. Numerous variations and elaborations have been explored, and a number have found practical application. 

This approach, suggested by D. J. Mead (22) and analyzed by Parfitt et al. 2Z, 23), and later by Plunkett and Lee (21) and by Zeinetdinova et al. (25), results in locally increased strains in the viscoelastic layer in the regions around the cuts, and therefore results in additional dissipation. Parfitt s experimental results... 

Figure 7. Maximum Loss Factor versus Stiffness Parameter for Constrained Viscoelastic Layer Treatments (Adapted from ref. 10)...

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. 

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