Natural resonance

The Weissenbetg Rheogoniometer is well suited to research on homogeneous viscoelastic fluids and elastic melts. For oscillatory shear a second motor-drive mechanism is added. This allows the use of 60 frequencies in the range of 7.6 x 10 to 40 Hz at ampHtudes between 2 x 10 and 3 X 10 rad. An electronic circuit improves the precision of oscillatory measurements, particularly at frequencies neat the natural resonance frequency of the instmment itself (298). 

Of all vibration frequeneies, the most dangerous are the synehronous vibrations, where an externally foreed vibration exeites one of the natural (resonant) frequeneies in the maehine. Campbell diagrams eonstrueted by the manufaeturers will help the operator avoid these frequeneies during run-up or eoimuissioning of tlie maehine in question. 

Quasi-resonant converters utilize an T-C tank circuit, which rings at its natural resonance frequency in response to a step change in its terminal voltage or current. The tank circuit is placed between the power switch and the transformer and/or the transformer and the output filter. 

Next, decide the natural resonance frequency of the tank circuit. For the available quasi-resonant controller ICs on the market, the range is between 1 and 2 MHz. This limit should be considered the maximum limit within conventional QR designs. So 1 to 1.5 MHz is a typical choice. Lower frequencies can be used and some efficiencies can be gained. The equation for the resonance frequency is... 

Key Words —Nanotubes, mechanical properties, thermal properties, fiber-reinforced composites, stiffness constant, natural resonance. 

A number of studies (Kristoff and Guilbault 1983 Milanko et al. 1992) have investigated the use of coated and uncoated piezoelectric crystals in the detection and analysis of diisopropyl methylphosphonate in air samples. Piezoelectric crystals have a natural resonant frequency of oscillation that can be utilized to detect... 

Ab initio electron correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities were reported for oxadiazoles <1996JPC8752>. The various measures of delocalization in the five-membered heteroaromatic compounds were obtained from MO calculations at the HF/6-31G level and the application of natural bond orbital analysis and natural resonance theory. The hydrogen transfer and aromatic energies of these compounds were also calculated. These were compared to the relative ranking of aromaticity reported by J. P. Bean from a principal component analysis of other measures of aromaticity <1998JOC2497>. 

The natural resonance theory (NRT) method53 offers a convenient ab initio means to calculate such resonance weights from the D(true) density matrix for a [Pg.32]

Natural resonance theory (NRT) allows these conflicting pictures of the oxyan-ion electron distributions to be tested quantitatively.149 Table 3.36 compares the geometries, NRT bond orders, atomic charges, and d-orbital occupancies for a representative variety of first- and second-row XOm"+ species,... 

Natural resonance theory (Section 1.6) provides a quantitative gauge of the contributions of various resonance structures to the total electronic density. The results are shown in Table 4.41 demonstrating the remarkable intermediacy in the nature of metal-alkene interaction relating metallacycle, nonbonded, and carbanion-type resonance forms. 

Because we are both computational chemistry researchers, we have naturally directed the book also to specialists in this field, particularly those wishing to incorporate natural bond orbital (NBO) and natural resonance theory (NRT) analysis into their methodological and conceptual toolbox. Researchers will find here a... 

In general for small P /Ph ratios, with (the resonant bubble radius), oscillations take place at approximately the excitation frequency (Fig. 2.21). For R > Rj, bubble oscillation has a strong component of its ovm natural resonant frequency (Fig. 2.22). However for very small bubbles, R. << R, transient conditions are attained as P increases beyond Pjj (Fig. 2.23, P = 4 and 10 atm). It may be that as... 

Thus on applying rapidly reversing charges to a piezoelectric material fluctuations in dimensions will be produced. This effect can be harnessed to transmit ultrasonic vibrations from the crystal section through whatever medium it might be in. However it is not possible to drive a given piece of piezoelectric crystal efficiently at every frequency. Optimum performance will only be obtained at the natural resonance frequency of the particular sample - and this depends upon its dimensions. In the... 

The SjN ratio increases with the square-root of the number of scans, provided that the NMR signals are perfectly reproducible (except for the receiver noise). In EEC, this is not always true due to the main field instabilities, which often exceed the natural resonance line-width of the sample. In such cases, the rule applies well to the starting portion of the FIDs but not... 

Once the tube scanner was invented (Binnig and Smith, 1986), it soon became the primary choice of piezo scanners in STM. Its small size and high natural resonance frequency make the mechanical design and vibration isolation much easier. Currently, most of the commercial STMs as well as home-made STMs use tube scanners. 

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