Pulse-propagation measurements

One example of a relatively new technique for the non-invasive, non-destructive characterization of network structures involves pulse-propagation measurements [288,289]. In this technique, the delay Af in a pulse passing through the network is used to obtain information on the network structure, for example, the chain length between cross-links or between entanglements. The technique is illustrated schematically in Figure 12 [282]. 

Another example of a relatively new technique for the noninvasive, nondestructive characterization of network structures involves ultrasound pulse-propagation measurements. The goal here is the rapid determi-... 

Newer techniques for characterizing elastomers include Brillouin scattering [43], and pulse propagation measurements [44]. 

Romanchenko and Stepanov (1981) recognized that the impulse imparted at the spall plane to material downstream, because of the elastic-plastic nature of this material, led to an attenuating tensile stress pulse propagating toward the sample-window interface as is illustrated in Fig. 8.9. Thus, the maximum tension inferred from the measured spall signal should be adjusted for this attenuation in estimating a material spall strength at the spall plane. 

Figure 12 Pulse propagation results, showing measurement of the time At required for a pulse to pass downward through an elastomer from Sensor 1 to Sensor 2. 

The sonic speed used was longitudinal wave speed, measured using a pulse propagation meter (Model 4, H. M. Morgan Co., Cambridge, Mass.). Pulse frequency was 8-10 kHz. Transverse wave velocity was calculated from longitudinal wave velocity using the approximation... 

Fig. 6.13. The polariton wavepacket, created by coherent scattering of picosecond laser and Stokes pulses, propagates in the crystal at the angle 0 with respect to the excitation direction. This angle is determined by the excitation wavevector geometry (see above). The coherent amplitude of the propagating wavepacket may be measured by phase-matched coherent anti-Stokes scattering of a probe pulse suitably delayed in time (fn) and displaced in space (by Xn)- Reprinted with permission from Gale et al. (68). Copyright (1986), American Physical Society.

Inevitably, the conjunction of frequency-dependent visco-elastic properties and wave propagation leads to consideration of visco-elastic wave dispersion and its influence on conventional wave-based measurements, such as those involving resonance phenomena and pulse propagation techniques. 

Recourse to pulse propagation measmements is often prompted by their apparent simplicity, involving measurements of the time-of-flight of a disturbance propagating through a visco-elastic material [Joseph et al, 1986]. 

Such simple measmements belie the complicating effects of visco-elastic wave dispersion, which may render their analysis unreliable. The tendency of pulse frequency components to travel at different velocities in dispersive media distorts the pulse, thereby influencing measurements of damping to a degree dependent on the mediiun and the spectral content of the pulse. The latter, in turn, depend on pulse shape. This visco-elastic wave dispersion, associated with dissipative stresses, can severely restrict the application of pulse propagation techniques in which the measmed velocity may correspond to a group velocity, U, not the requisite phase velocity, v. As U and v may differ... 

The longitudinal sound speed in the polymer can be determined by measuring the time required for a pulse propagated normally into the sample to reflect from its far surface (usually a polymer/air interface where the impedance mismatch generates a reflected wave), and dividing the sample s thickness by twice this time. The time is determined by the interval between the initial pulse and the successive reflections, which result as the wave bounces... 

T. NOMURA, S. GOTOH, and K. YAMAKI, Reactivity Measurements by the Two-Detector Cross-Correlation Method and Siqpercritical Reactor-Noise Analysis, Neutron Noise, Waves and Pulse Propagation, ABC Symp. Ser. 9, CONF-660206 (May 1967). 

The distributed signals can be measured and spatially resolved by an optical time-domain reflectometry technique. An optical time domain reflectometer is based on the measurement of backscattered light attained from a light pulse propagating through an optical fiber. Light is backscattered because of inhomogeneities and impurities... 

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 ... 

For studies of dilute polymer solutions, measurements of high precision are necessary to obtain the small differences between the properties of solutions and solvent. Apparatus for pulse propagation in such solutions at 20 MHz has been described by Miyahara, Wada, and Hassler," and for variable path interferometry by Cerf, and for standing waves by Miyahara. jjj jjjg latter method, the frequency can be varied continuously from 1 to 20 MHz. At lower frequencies (10 to 700 kHz), the free decay of waves in a spherical vessel can be measured. In such measurements, the data are ordinarily left in terms of M (or simply velocity and attenuation, or the acoustic absorption coefficient identified in Chapter 18) with no attempt to convert them to K. ... 

The measurement of the extensional modulus was re-examined as a possible method for the measurement of molecular orientation in textile yarns by Charch and Moseley [28], Moseley [29] and Morgan [30], Morgan has developed Hamburger s pulse-propagation method. 

The version of the apparatus used nowadays was introduced by Kolsky (1963), who added a second bar, from which the name Split Hopkinson Pressure Bar comes from the specimen of material to be tested is inserted between the two bars, as shown schematically in O Fig. 21.5a. The projectile, usually fired by means of a pneumatic gun, impacts the first bar (incident bar), generating the incident pulse which, at the bar/specimen interface, is partially reflected and partially propagates in the specimen. From the specimen, the pulse is transmitted to the second bar (transmitter bar). The situation is described graphically by the so-called Lagrangian diagram presented in O Fig. 21.5b. A concrete example of Split Hopkinson pressure bar is shown inO Fig. 21.6. The pulses are measured by means of strain gages placed on both incident and transmitter bar thus, their time history can be stored by means of a transient recorder, usually a digital oscilloscope or an acquisition board. From such measurements the stress (a), strain (e), and strain rate (s) in the specimen can be obtained as... 

Usually, the depolarization current is measured to avoid the dc conductivity contribution. The dielectric relaxation spectrum is then obtained by Fourier transform or approximate formulas, e.g., the Hamon approximation [14]. By carefully controlling the sample temperature and accurately measuring the depolarization current, precision measurements of the dielectric permittivity down to 10" Hz are possible [18]. In fast time domain spectroscopy or reflectometry, a step-like pulse propagates through a coaxial line and is reflected from the sample section placed at the end of the line. The difference between... 

Typical waveform of a THz pulse propagating through air (t), measured by electro-optic sampling. Fourier-transforming the time-domain waveform 5uelds the spectral amphtude and the phase of the THz eleetric field. 

In Chapter 7, the thermal properties of carbon nanotubes are discussed by M. Osman, A. Srivastava and D. Srivastava. The authors first present the physical structure of nanotubes and their electrical properties. Then, theoretical analytical approaches to thermal conductivity and specific heat calculations are introduced. This is followed by a review of the recent experimental measurement of thermal conductivity of single-wall nanotubes (SWNTs) and multiwall nanotubes. They also present a molecular dynamical simulation approach and its application to the investigation of thermal conductivity of SWNTs, Y-junction nanotubes and heat pulse propagation in SWNTs. 

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