Lambe

Interdigital Lamb Wave Transdusers for Rapid Monitoring of Plate Structures. 

PVDF film is readily commercially available in thicknesses up to 110 pm. If film of this thickness is bonded to a rigid substrate, the peak response is at a frequency of about 3.7 MHz which corresponds to the thickness of the layer being a quarter wavelength. This frequency is rather high for most Lamb wave testing since Fig 1 shows that even on a I mm thick... 

R. S.C. Monkhouse, P.D. Wilcox and P. Cawley, Flexible Interdigital PVDF transducer for the generation of lamb waves in structures. Ultrasonics (in press). 

Based upon a piezoelectric 1-3-composite material, air-bome ultrasonic probes for frequencies up to 2 MHz were developped. These probes are characterized by a bandwidth larger than 50 % as well as a signal-to-noise ratio higher than 100 dB. Applications are the thickness measurement of thin powder layers, the inspection of sandwich structures, the detection of surface near cracks in metals or ceramics by generation/reception of Rayleigh waves and the inspection of plates by Lamb waves. 

Generation and Detection of Lamb Waves for Plate Inspection... 

The use of Lamb waves offers the possibility of rapid long-range in-service inspection. Receiver and transmitter probes are positioned single sided - access is only required from one side of the specimen - in a pitch-catch-arrangement, the receiver being outside tbe field of the specular reflection. 

Castaings, M. and Cawley, P. The generation, propagation, and detection of Lamb waves in plates using air-coupled ultrasonic transducers... 

Figure Bl.4.5. The Lamb dip spectrum of the CO 6-5 transition obtained with the Cologne THz BWO spectrometer. The dip is of order 30-40 kHz in width and the transition frequency is detennined to 0.5 kHz [M].

The two primary causes of shielding by electrons are diamagnetism and temperature-independent paramagnetism (TIP). Diamagnetism arises from the slight unpairing of electron orbits under the influence of the magnetic field. This always occurs so as to oppose the field and was first analysed by Lamb [7]. A simplified version of his fomuila. 

Kratschmer W, Lamb L D, Fostiropoulos K and Huffman D R 1990 Solid Cggj a new form of oarbon Nature 347 354-8... 

Lamb G L Jr 1980 Eiements of Soiiton Theory (New York Wiley)... 

A further preliminary statement to this section would be that, somewhat analogously to classical physics or mechanics where positions and momenta (or velocities) are the two conjugate variables that determine the motion, moduli and phases play similar roles. But the analogy is not perfect. Indeed, early on it was questioned, apparently first by Pauli [104], whether a wave function can be constructed from the knowledge of a set of moduli alone. It was then argued by Lamb [105] that from a set of values of wave function moduli and of their rates... 

Figure 2.5 Typical (gaussian) absorption line showing a HWHM (half width at half maximum) of Av and a Lamb dip (dashed curve)...

Natural line broadening is usually very small compared with other causes of broadening. However, not only is it of considerable theoretical importance but also, in the ingenious technique of Lamb dip spectroscopy (see Section 2.3.5.2), observations may be made of spectra in which all other sources of broadening are removed. 

Figure 2.6 Three typical groups of molecules, with velocities (molecules 1 and 2), 0 (molecules 3-5), and —v (molecules 6 and 7) towards the source in a Lamb dip experiment...

Molecules such as 3,4 and 5 in Figure 2.6, which have a zero velocity component away from the source, behave uniquely in that they absorb radiation of the same frequency Vj-es whether the radiation is travelling towards or away from R, and this may result in saturation (see Section 2.3.4). If saturation occurs for the set of molecules 3, 4 and 5 while the radiation is travelling towards R, no further absorption takes place as it travels back from R. The result is that a dip in the absorbance curve is observed at Vj-es, as indicated in Figure 2.5. This is known as a Lamb dip, an effect which was predicted by Lamb in 1964. The width of the dip is the natural line width, and observation of the dip results in much greater accuracy of measurement of v es. 

In 1947 Lamb and Retherford observed the 2 P j2 transition using microwave... 

Figure 9.24 Laser Stark spectrum of FNO showing Lamb dips in the components of the line of the ij vibrational transition. (Reproduced, with permission, from Allegrini, M., Johns, J. W. C. and McKellar, A. R. W., J. Molec. Spectrosc., 73, 168, 1978)...

A further feature of the spectmm in Figure 9.24 is the sharp spike at the centre of each P-shaped transition. The reason for this is that saturation of the transition has occurred. This was discussed in Section 2.3.5.2 in the context of Lamb dips in microwave and millimetre wave spectroscopy and referred to the situation in which the two energy levels involved, m(lower) and n(upper), are close together. Under these circumstances saturation occurs when... 

Figure 9.26 (a) Doppler line shape with a Lamb dip. (b) As in (a) but with modulation and phase-... 

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