Viscoelastic resonant conditions

Probing Viscoelastic Films that Approach Resonant Conditions. 443... 

The occurrence of yam breaks was reported early and is connected with thickness fluctuations in extruded ribbons or films, as described collectively by the phenomenon of draw resonance , which is characterized by oscillations of the fiber diameter, which ultimately lead to yarn break. The latter is defined as brittle fracture and is thus related to melt temperature, molecular weight, quenching conditions, and particularly to the role of viscoelasticity, as described in the following section. 

Since the transverse shear wave may penetrate the damping surface layer and the viscous liquid, additivity of the equivalent electrical elements in the BVD circuit is only valid under certain particular conditions. Martin and Frye [53] studied the impedance near resonance of polymer film coated resonators in air with a lumped-element BVD model, modified to account for the viscoelastic properties of the film. In addition to the elements shown in Fig. 12.3 to describe the quartz crystal and the liquid, L/ and Rf were added to describe the viscoelastic film overlayer. For a small... 

Figure 6a shows the transmission hne representing a viscoelastic layer [64]. Every layer is represented by a T . The apphcation of the Kirchhoff laws to the Ts reproduces the wave equation and the continuity of stress and strain. The detailed proof is provided in [4]. To the left and to the right of the circuit are open interfaces (ports). These can be exposed to external shear waves. They can also be connected to the ports of neighboring layers (Fig. 6b). Alternatively, they may just be short-circuited, in case there is no stress acting on this surface (left-hand side in Fig. 6c). Finally, if the stress-speed ratio Zl (the load impedance, see below) of the sample is known, the port can be short-circuited across an element of the form AZl, where A is the active area (right-hand side in Fig. 6c). Figure 6c shows a viscoelastic layer which is also piezoelectric. This equivalent circuit was first derived by Mason [4,55]. We term it the Mason circuit. The capacitance, Co, is the electric capacitance between the electrodes. The port to the right-hand side of the transformer is the electrical port. The series resonance frequency is given by the condition that the impedance of the acoustic part (the stress-speed ratio, aju) be zero, where the acoustic part comprises all elements connected to the left-hand side of the transformer.

In a car ully designed high quality resonator, the dissipation processes 2), 3), and 4) can be kept negligibly small. It is important to minimize the perturbations caused by these effects, because a theoretical treatment is difficult. It was shown in Ref. and that such an optimization of the cell is in fact possible and then only viscous and thermal boundary layer losses ne be taken into account. Throughout the principal portion of the volume of the resonator, the expansion and contraction of the gas occurs adiabatically. Near the walls, however, this process becomes isothermal. This leads to heat conduction, which is responsible for the thermal dissipation process. The viscous dissipation can be explained by the boundary conditions imposed by the wails. At the surface, the tangential component of the acoustic velocity is 2 0, whereas in the interior of the cavity, it is proportional to the gradient of the acoustic pressure. Thus, viscoelastic dissipation occurs in the transition region. 

In the present study, as a first step toward the evaluation of human brain stiffness using a tactile resonance sensor, we determined the standard values of the transcutaneous viscoelastic properties near cranial defects under stable conditions before cranioplasty. 

This study was approved by the ethics committee of Shimane University Hospital (IRB 475). The background populations were inpatients admitted for unilateral decompressive craniectomy (DC), which prevents brain herniation due to acute intracranial hypertension, at our institution between 2006 and 2010. In this study, seven subjects underwent transcutaneous measurements of viscoelastic properties through cranial defects by a tactile resonance sensor and CT scans within three days before cranioplasty, which was most often done around one month after DC. Their transcutaneous viscoelastic properties via the cranial defects were determined under normal conditions. 

Our goal was to measure the viscoelastic properties of the human brain under practical conditions. Therefore, we used the tactile resonant sensor with the stress-strain function that simulated manual palpation. In this study, the stiffness was 2.837 0.709 (N), Young s elastic modulus was E = 5.08 1.31, and the shear modulus was G = 1.94 0.49 for a depth of 3.0 mm. Poisson s ratio (u) was calculated as 0.31-0.62 using the equation E = 2G (1h- u). These values were approximately equal to those previously reported for the viscoelasticity properties of the brain in vivo [1-7]. The results of indentation fitted the Maxwell model as expressed by the equation G = Ge - Gi exp (-t/x), where Ge is the instantaneous modulus in shear, Gi is the relaxation in the shear modulus, t is time, and x is the relaxation time. Thus, G = 1.94-1- 3.3 exp(-t/0.5) under the assumption that Ge = 1.94, Gi = 3.3, t = h/1.5, and x = 0.5. The results obtained in this study by an indentation method, reflected those of a previous model [9-12]. However, this measurement method evaluated brain viscoelasticity via multiple structural layers including the skin, subcutaneous tissues, muscle fascia, and dura. Moreover, some assumptions had to be made to approximate the expression for elasticity. 

Solution. At a draw ratio of 10 and power-law index of 1/3, Figure 9.14 shows that the minimum and the maximum attainable values of the viscoelastic parameter a /" are 0.043 and 0.1, respectively. The velocity at zero axial distance is given as 7.09 cm/s. Thus, the parameter a /" is calculated as 0.027, which is outside the limits of 0.043 and 0.1. Melt spinning with these conditions is expected to result in draw resonance. To get rid of this problem we need to decrease the spinning length to about 180 cm. ... 

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