No abstract

No abstract

An analysis is made of the feasibility of measuring the viscoelastic properties of materials having a loss factor greater than 1. A conclusion is made as to the suitability of a two-parameter method for measuring the properties of such materials at phase angles 0 > 100 ~ Diagrams of the strains and the [2]. The method is based on measurement of the ratio of the amplitudes A and phase shifts O of the vibrational accelerations of the top and bottom surfaces of a specimen loaded by a mass M, as shown in Fig. 1. When the length of the deformation wave is much greater than the height of the specimen, the elastic modulus E and the loss factor r/are related to the parameters measured in the experiment in the following manner [1]:where H and F are the height and cross-sectional area of the specimen; ~0 is the angular frequency of vibration. It was shown in [3, 4] that this condition is satisfied at n < 0.64 throughout the range of parameters measured if M/m > 30 (where m is the mass of the specimen). Here, the difference'from the exact solution is no greater than 1%. Graphs of the corrected coefficients and their approximation formulas were presented for the case M/m > 30. However, the region of high loss factors (r/ _> 0.5) is most important for sound-insulating and sound-absorbing materials, since this is the range within which these materials are normally used.The standard [2] does not require determination of the resonance frequency of specimen vibration or measurement of the ratio of the vibrational accelerations of the top and bottom surfaces of the specimen at this frequency. It can be seen from the amplitude-phase characteristic of the vibrations (Fig. 2) that it is difficult to find the resonance frequency as the loss factor increases, since the resonance peak becomes more diffuse. The error of determination of elastic modulus increases even more, since E -0: 2. The resonance frequency (phase 00 = ~'/2 -arctan rl) decreases with an increase in r/: 0 o = 45 ~ at 7/ = 1 and 00 = 8.2 ~ at ~7 = 8. It is nearly impossible to determine the resonance frequency at 7/ > 1, which limits the range of application of the method [2]. Thus, it can be concluded that the usefulness of the method is heavily dependent on the resonance characteristics of the system.The two-parameter method [1] being proposed for use here is free of this restriction, since it does not require determination of the resonance frequency. However, as can be seen from Fig. 2, the amplitude -phase characteristics converge in the regions of their respective resonance frequencies and become difficult to distinguish. If rl > 4, then the measurements should be made at 0 > 100 ~ In this range, materials with different loss factors differ in the ratio of the vibrational accelerations of the top and bottom surfaces. However, the expanded range of application of the given method comes at the expense of a reduction in the strength of the signal from the upper transducer by a factor of 5-10. The method can still be used despite this reduction.

The duration of the portions of coherence of turbulent pressure pulsations is determined experimentally. Based on this the dimensionless rate of deformation of the surface of a pliable coating is calculated with allowance for its inertial properties.Interest in studying pliable coatings was provoked by a series experiments of Kramer [1]. His coatings imitated the skin of dolphins, which can swim at an abnormally high speed. Kramer assumed that the coating damps Tollmin-Schlichting waves and thereby delays the transition to turbulence.Benjamin [2] assumed that a pliable coating can reduce friction in turbulent flow, modifying its boundary layer, but the character of the flow itself remains turbulent. Indeed, in Kramer's experiments, too, the turbulent friction was, apparently, reduced since there was a turbulizer in the forepart of his model. Many schemes of pliable coatings, a classification of which is proposed in [3], have been put forward and tested in the ensuing years. The greatest attention was paid to passive coatings deformed by turbulent pressure pulsations.To explain the friction reduction in a developed turbulent flow, two hypotheses have currently been developed. The first considers the propagation of deformation waves over the coating surface that are caused by the pressure pulsations on the wall. The friction reduction is associated with energy dissipation inside the wall. In the most developed theory [4], one predicts parameters of the coating material for which unstable deformations of the surface do not occur.The second theory [5] assumes that the coating is locally deformable. This means that running waves do not propagate from the site of application of the periodic deformation. The friction reduction is related to a change in the pattern of generation of Reynolds stresses (puv) in the wall region. Such a change is quite possible, since the component of the pulsating velocity v that is normal to the wall can change in both magnitude and phase because of deformation of the wall by the turbulent pressure pulsations. So far, neither theory can calculate the friction reduction; they are capable only of predicting the region of the parameters of the coating material where friction reduction is possible.In [6], a material whose properties are calculated according to the Duncan theory is used and a decrease in the turbulence intensity, coefficient of friction, and Reynolds stresses is obtained. Coatings calculated according to the Semenov theory turned out to be much more rigid but showed a decrease of up to ---17% in the friction and the level of pressure pulsations [7]. Tests of these coatings in a cavitation tunnel at the University of Newcastle carried out by independent researchers [8] using more sophisticated measuring equipment conf'umed the validity of the previous neasurements.Thus, there are two alternatives at present: "soft" coatings with running waves and locally deformable "rigid" coatings. To describe the operation of both coatings, we must know the manner in which the coating surface i...