Plate-wave velocity

In general, detonation test apparatus consists of a steel tube that is filled with the substance under investigation. One end of the tube is provided with a booster charge consisting of an electric detonator covered by detonative material. The other end is either closed or provided with a witness plate. One type of steel tube apparatus is provided with a velocity probe to record the shock wave velocity as shown in Figure 2.28. 

Description of exptl procedures is given on pp 1930-34 of Ref 15a. A schematic, arrangement for delivery of plane shock wave and for measuring shock-wave velocities for shock strengths from 10 to 90 kbar in the specimens and the free-surface velocity of the specimen plate is shown in Fig 2,. p 1930. 

The various shock-producing systems were calibrated by using free-surface velocity measurements of specimen plates and corresponding shock-wave velocities obtd from the known equations of state of the specimen plate materials. Accdg to Footnote 4 on p 1931 of Ref 15a, the free-surface velocity for a plane shock wave is almost twice the particle velocity"... 

An experimental arrangement is illustrated in Fig 1. on p 381 of Ref 93. A metal plate thickness , is bent thru an angle deton wave, velocity DQ travelling thru a layer of explosive. When the plate was deflected, it hit at an angle of incidence i a block of expl, density p.Q The thicknesses were sufficiently small compared to the other quantities so that the flow could be considered as plane two-dimensional and stationary. The reference system R had its origin at the point of impact I and was under uhiform linear motion. Theoretical and experimental studies of the flow were carried ont in the vicinity of the noinr nf impact... 

The wavelength of linear or low-amplitude sound in water [m] is X = c/v. Here, the wave velocity c is approximately 1500 m/sec, and v is the frequency in Hertz. Sound from a flat source (called a piston source if round, or a plate source if rectangular) does not retain the shape of the source as it propagates away, but spreads out fairly predictably. The rate of this spreading is often stated as the beamwidth, which means the width of a cone [°], that contains one-half the power of the beam. This width of this cone follows the relationship sin(0) = Xjd, where dis the diameter or width of the source [m]. However, this equation loses its utility for d smaller than one... 

Equation 3.63 gives an approximation for the SH plate-mode spectrum found in an unperturbed quartz plate. The presence of surface features, including transducers, perturbs the wave velocity, and hence the excitation frequency, of each mode. 

In a flexural plate wave (FPW) device, an acoustic wave is excited in a thinned membrane. Figure 3.38 (page 112). As with the other acoustic sensors discussed — the TSM, SAW and APM devices — the flexural-plate-wave (FPW) device can sense quantities that cause its phase velocity, Vp, to change. A unique... 

Figure 339 Symmetric (S) and anti-symmetric (A) Lamb wave characteristics. Vertical axis Lamb-wave velocity normalized to transverse bulk-wave velocity. Horizontal axis Product k4 where kt = transverse wavenumber = 27r/At, where At is transverse wavelength and d is plate thickness. (Reprimed with permission. See Ref. [61]. 1967 Plenum Press.)...

The phase velocity of the So mode is maximum for a very thin plate, and it falls as d/A increases, finally becoming asymptotic from above to the surface-wave velocity for the medium. 

The rise in (2) is due to the increased effective stiffness of the medium as an ever-thickening plate is required to assume the sinusoidal wave shape. The approach to the surface-wave velocity as the plate becomes thick is to be expected, as a surface wave can be represented as a superposition of antisymmetric and symmetric plate waves. The particle motions that are indicated schematically by the ellipses near the curves of Figure 3.40 are predominantly normal to the plate for the Aq mode and predominantly tangential to the plate for the So mode. 

Figure 3.40 Calculated phase velocity of flexural plate waves vs ratio of plate thickness, d, to wavelength. A, for silicon nitride. Material is assumed to have the elastic properties of Si3N4 and no residual tension. The mode shapes ate illustrated at the right with a greatly enlarged vertical scale for clarity. Ellipses at left show the retrograde elliptical particle motions of the lowest S3rmmetric and antisymmetric modes for d/A = 0.03. (Reprinted with pemtission. See Ref. (621.)...

APM) phase velocity of plate wave phase velocity of shear wave jc-component of particle velocity in liquid value of Vjc at surface of crystal three particle velocity ccnnponents at surface (for SAW) propagation velocity (for SAW)... 

Acoustic Streaming, Fig. 6 Distributions of the Stokes drift velocity across the fluid layer for three channel depths given by the flexural plate wave... 

The other group of methods includes those that are based on the registration of the state originated after the shock wave reflection from a barrier. For instance, the detonation pressure m be determined on the basis of the measurement of a thin metal plate firee-surface velocity. The plate free-surface velocity can be determined using optical methods or the electrocontact type of probes and oscilloscope technique. The methods based on the determination of the shock wave velocity through an inert material, e.g., the Aquarium test, are also included in this group. The time resolution of these methods may be on a nanoseconds scale, and even less than a nanosecond, e.g., w en laser interferometry technique is used. Since the processes in the shock fi-ont occur on a nanosecond scale, the present-day techniques are still inadequate to study the detonation wave shock front. 

BF-RAREFACTION WAVE REFLECTED IN METAL PLATE tana-DETONATION VELOCITY tanp-SHOCK WAVE VELOCITY IN METAL PLATE... 

The signals, produced by the electric circuit closure by electrocontact probes, are led and then recorded Ijy oscilloscope. When the oscillogram thus obtained is treated, as described in Subsection 4.1.4, the shock wave velocity (C/ ) in the metal plate may be obtained. 

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