Viscoelasticity wave propagation methods

The theories of elastic and viscoelastic materials can be obtained as particular cases of the theory of materials with memory. This theory enables the description of many important mechanical phenomena, such as elastic instability and phenomena accompanying wave propagation. The applicability of the methods of the third approach is, on the other hand, limited to linear problems. It does not seem likely that further generalization to nonlinear problems is possible within the framework of the assumptions of this approach. The results obtained concern problems of linear viscoelasticity. 

Although part of Chapter 16 is devoted to wave propagation in viscoelastic materials and some specific simple cases are studied in detail as part of the engineering applications of viscoelasticity, it is useful to mention here that there are several experimental methods to determine the dynamic response... 

It was these studies of the complex dielectric constant as a function of frequency which led to the search for euialogous methods of studying viscoelasticity hy measuring a complex viscosity or elastic modulus. The first success was observation of shear wave propagation in polymer solutions . The only theoretical treatment of wave propagation which could he found as a clue to analysis of the measurements was in a geophysical journal. From the wave propagation the complex shear modulus and its frequency dependence could be derived. 

Nonlinear soil behavior can be approximated by an equivalent linear characterization of soil dynamic properties. The method makes use of the exact continuum solution of wave propagation in horizontally layered viscoelastic materials subjected to vertically propagating transient motions (e.g., Roesset 1977). It models the nonlinear variation of soil shear modulus and... 

Acoustic Measurements. Measurement of the propagation of ultrasonic acoustic waves has been found useful for determining the viscoelastic properties of thin films of adhesives. In this method, the specimen is clamped between transmitting and receiving transducers. The change in pulse shape between successive reverberation of the pulse is dependent on the viscoelastic properties of the transmitting material. Modulus values can be calculated (267,268). 

In the methods of the preceding section, the propagation of a shear wave into the viscoelastic liquid is not observed directly only its effect on the propagating surface is detected and measured. On the other hand, if the damping is not too severe, so that a wave train of several maxima and minima is perceptible, the wavelength and attenuation can be measured directly, as described in this section. The sample must be sufficiently large so that the waves are attenuated before they can experience reflection. 

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