Vibration torsion

Translation and rotation Translation, rotation, torsion Translation, rotation, torsion, vibration... 

Figure 6.13 Illustration of (a) rocking, (b) twisting, (c) scissoring and (d) wagging vibrations in a CH2 group. Also shown are (e) the torsional vibration in ethylene, (f) the ring-breathing vibration in benzene and (g) the inversion, or umbrella, vibration in ammonia...

It should also be remembered that the selection mles derived here are relevant to the free molecule and may break down in the liquid or solid state. This is the case, for example, with the electric dipole forbidden 4q transition in ethylene, where V4 is the torsional vibration shown in Figure 6.23. It is not observed in the infrared specttum of the gas but is observed weakly in the liquid and solid phases. 

The vibrations of acetylene provide an example of the so-called mutual exclusion mle. The mle states that, for a molecule with a centre of inversion, the fundamentals which are active in the Raman spectmm (g vibrations) are inactive in the infrared spectmm whereas those active in the infrared spectmm u vibrations) are inactive in the Raman spectmm that is, the two spectra are mutually exclusive. Flowever, there are some vibrations which are forbidden in both spectra, such as the torsional vibration of ethylene shown in Figure 6.23 in the >2 point group (Table A.32 in Appendix A) is the species of neither a translation nor a component of the polarizability. 

Figure 6.44 Torsional vibrations in (a) toluene, (b) phenol, (c) ethylene, (d) methyl alcohol, (e) s-lraws-buta-l,3-diene and (1) s-cis-buta-l,3-diene...

Table 6.7 Barrier heights V for some torsional vibrations...

Sketch the form of the potential energy as a function of torsional angle cj) for the torsional vibration in (a) ethane, (b) CH3NO2, (c) 2-fluorophenol, (d) CH2FOH, and... 

In the chapter on vibrational spectroscopy (Chapter 6) 1 have expanded the discussions of inversion, ring-puckering and torsional vibrations, including some model potential functions. These types of vibration are very important in the determination of molecular structure. 

Torsional vibration can also be a problem and results from pressure variations in the cyhnders which can produce cyclic torques with harmonics ranging from half speed to 10 or 12 times running speed. 

The measured dependence of kn(T) and T) consists of an Arrhenius region ( = 9.6 kcal/mol) going over to the low-temperature plateau below IlOK, where k 10 s . The isotope effect grows as the temperature drops, kn/ko — 20 at T = 100 K (fig. 15). Tunneling is promoted by the torsional vibrations of the OH and CH groups, as well as the oxy-group bending vibration. 

The fine structure of torsion-vibration spectra of small symmetric molecules and groups such as CH3, CH4, NH3, and NH4 is one of the most illustrative manifestations of tunneling. This problem has been discussed in detail in several reviews and books (see, e.g., Press [1981], Heidemann et al.[1987]). 

Fig. 49. Correlation between the energy levels of (1) free rotation of the symmetric top, and (2) torsion vibrations in the potential with symmetry Cj. Quantum numbers J and K enumerate rotational levels, n vibrational levels. Relative positions of A and E levels are shown on the right.

Wright, J., A Practical Solution to Transient Torsional Vibration in Synchronous Motor Drive Systems, American Society of Mechanical Engineers, Pub. 75-DE-15. 

Kerr Wilson, W., Practical Solution of Torsional Vibration Problems, Vols. 1 II, London Chapman Hall, Ltd., 1956. 

Brown, Royce N, A Torsional Vibration Problem as Associated wjih Synchronous Motor Driven Machines, ASME 59-A-141, Journal ofEngi-ntcring for Power, Transactions of the ASME, New York American Son et of Mechanical Engineers, 1960, pp. 215-225. 

Hi/ume, A., Transient Torsional Vibration of Steam Turbine and Generators Shafts due to High Speed Reclosing of Electric Power Lines, ASME... 

Holdrege, J. H., Subler, William, and Frasier, William E, A C. Induction Motor Torsional Vibration Consideration —A Case Study, IEEE Paper No. PCT8/-2, pp. 23-27. 

Pollard, Eniest 1., Synchronous Motors. . . Avoid Torsional Vibration Problems, Hydrocarbon Processing, February 1980, pp. 97-102. 

Pollard, Ernest L, Torsional Vibration Due to Induction Motor Transient Starling Torque, undated manuscript. 

Drehungs-grad, m. degree of rotation, -kraft, /, rotatory power, -schwingtmg, /, torsional vibration, -streuung, /, rotatory dispersion, -vermogen, n, rotatory power, -winkel, m. angle of rotation. 

For all types, avoiding torsional vibration problems is essential. 

Pollard, E. L, Synchronous Motors—Avoid Torsional Vibration Problems, Hydrocarbon Processing, p. 97, Eeb. (1980). 

Lateral vibrations result from the coupling with axial mode of buckling. The lateral vibrations may also result from a coupling with the torsional vibrations. 

Torsional vibrations are due to the stick-slip effect of the stabilizers in deviated boreholes. They can be seen at surface as large torque oscillations with a period of 3 to 10 s. Figure 4-308 shows a near-bit stabilizer in a deviated borehole. The stick-slip effect increases with WOB and RPM. 

Fig. 4 Raman spectrum of the external and torsional vibrations of a single crystal of a- Sg (resolution <0.1 cm ), after [110]...

Tables Assignment and wavenumbers (cm ) of the external and torsional vibrations of a-Ss based on polarization dependent studies [106, 107]. In the first two columns the type and symmetry classes of the molecular and crystal vibrations, respectively, are given. The wavenumbers of the vibrations are listed in the columns infrared and Raman corresponding to the order of symmetry species given in the second column (crystal). " S means orthorhombic Sg with natural isotopic composition, while stands for isotopically pure Sg crystals (purity >99.95%)... 

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