Wave propagation measurements

FIG.8-2. Apparatus for longitudinal bulk wave propagation measurements, by echoing longitudinal pulses through a liquid with and without a polymeric sample in the path. (Nolle and Mowry.p ... 

FIG.8-4. Apparatus for longitudinal bulk wave propagation measurements in a viscoelastic liquid, with variable path length. (Mason, Baker, McSkimin, and Heiss. )... 

We assume that in (4.38) and (4.39), all velocities are measured with respect to the same coordinate system (at rest in the laboratory) and the particle velocity is normal to the shock front. When a plane shock wave propagates from one material into another the pressure (stress) and particle velocity across the interface are continuous. Therefore, the pressure-particle velocity plane representation proves a convenient framework from which to describe the plane Impact of a gun- or explosive-accelerated flyer plate with a sample target. Also of importance (and discussed below) is the interaction of plane shock waves with a free surface or higher- or lower-impedance media. 

At this point it is useful to define the velocity of a sound (/ or b) wave propagating in a moving medium, which may also be compressed. The velocity with respect to stations moving with the medium is termed Lagrangian, C. The position of a station (for the purpose of calculating the velocity) is taken to be specified by its initial position. Sound velocity with respect to distances, measured with respect to the laboratory, is termed Eulerian, C . 

The fluid mechanics origins of shock-compression science are reflected in the early literature, which builds upon fluid mechanics concepts and is more concerned with basic issues of wave propagation than solid state materials properties. Indeed, mechanical wave measurements, upon which much of shock-compression science is built, give no direct information on defects. This fluids bias has led to a situation in which there appears to be no published terse description of shock-compressed solids comparable to Kormer s for the perfect lattice. Davison and Graham described the situation as an elastic fluid approximation. A description of shock-compressed solids in terms of the benign shock paradigm might perhaps be stated as ... 

Fig. 2.1. The traditional approach to the study of mechanical responses of shock-compressed solids is to apply a rapid impulsive loading to one surface of a diskshaped sample and measure the resulting wave propagating in the sample. As suggested in the figure, the wave shapes encountered in shock-loaded solids can be complex and may require measurements with time resolutions of a few nanoseconds.

For mechanical wave measurements, notice should be taken of the advances in technology. It is particularly notable that the major advances in materials description have not resulted so much from improved resolution in measurement of displacement and/or time, but in direct measurements of the derivative functions of acceleration, stress rate, and density rate as called for in the theory of structured wave propagation. Future developments, such as can be anticipated with piezoelectric polymers, in which direct measurements are made of rate-of-change of stress or particle velocity should lead to the observation of recognized mechanical effects in more detail, and perhaps the identification of new mechanical phenomena. 

Figure 3.64 Measured and calculated pressure wave propagation velocity in air-water mixtures at 25 psia. (From Henry et al., 1969. Copyright 1969 by Plenum Publishing, New York. Reprinted with permission.)... 

At high frequencies of 104 to 107 Hz, Young s modulus of fibers and film strips can be measured by wave propagation techniques (16,49-53). An appropriate equation when the damping is low is... 

Ryanodine receptors can be blocked by exposing the cells to 10 /iM ruthenium red. Under these conditions, oxytocin exposure still elicits Ca2+ waves, and the observed wave speeds are the same as waves measured in the absence of ruthenium red (Young Zhang 2001). Thus, similarly to InsP3 receptors, functional ryanodine receptors are not rate limiting in the mechanism of Ca2+ wave propagation. 

The elastic properties of PS depend on its microstructure and porosity. The Young s modulus for meso PS, as measured by X-ray diffraction (XRD) [Ba8], acoustic wave propagation [Da5], nanoindentation [Bel3] and Brillouin spectroscopy [An2], shows a roughly (1-p)2 dependence. For the same values of porosity (70%), micro PS shows a significantly lower Young s modulus (2.4 GPa) than meso PS (12 GPa). The Poisson ratio for meso PS (0.09 for p=54%) is found to be much smaller than the value for bulk silicon (0.26) [Ba8]. 

Equation (4.4) stresses that the surface plasma wave propagates within the aluminium substrate whose frequency is modified by the dielectric response of the molecular adlayer. From the measurements reported, with hcog = 8.5 eV and hcob = 15 eV, one obtains e = 2.1 for CuPc, a value in agreement with those measured for other planar organic molecules, with an extended delocalization of 7T-electrons (Alonso et al, 2003). 

Addnl Refs A) Collective, "Air Burst in Blast Bombs . A Compilation of Papers Presented at NDRC Div 2 Symposium, OSRD 4923 (1945) B) Collective, "Underground Explosion Test Program , Final Rept, Vol II, "Rock , Engineering Research Associates, Division of Remington Rand Inc, 30 April 1953 (Conf) (Not used as a source of information) C) G.R. Pickett, "Seismic Wave Propagation and Pressure Measurements Near Explosions , Quarterly of the Colorado School of Mines 50(4) (Oct 1955) D) W.E. Deal, "Shock Hugoniot in Air , JApplPhys 28, 782-84(1957) E) Dunkle s Syllabus, Session 26, 23 Apr 1958, pp 313-18 F) Dunkle s Syllabus, Suppl to Section 26 (1961) G) Dunkle, private communication,... 

---