Torsion-vibration coupling

Torsional flexing and related torsion-vibration-coupling effects... 

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

As in the simple 3- or 4-point bending of a beam the vibrating reed device assumes the validity of the differential Eq. (2.2) which is due to Euler. Timoshenko25 included both rotary inertia and shear deformation deriving a more exact differential equation which reduces to the Euler equation as a special case. Use of the Timoshenko beam theory for anisotropic materials has been made by Ritchie et al.26 who derive a pair of equations for torsion-flexure coupling (which will always occur unless the axis of the beam coincides with the symmetry axis of the anisotropic material). 

Inversion doubling has been observed in microwave spectrum of methylamine CH3NH2. This splitting depends on the quantum numbers of rotation and torsion vibrations [Shimoda et al., 1954 Lide, 1957 Tsuboi et al., 1964]. Inversion of NH2 alone leads to the eclipsed configuration corresponding to the maximum barrier for torsion. Thus, the transition between equilibrium configurations involves simultaneous NH2 inversion and internal rotation of CH3 that is, inversion appears to be strongly coupled with internal rotation. The inversion splits each rotation-vibration (n, k) level into a doublet, whose components, in turn, are split into three levels with m = 0, 1 by internal rotation of the... 

ZERBI questioned Rush as to whether the neutron diffraction results on torsional vibrations in solid o-xylene and durene indicate dispersion of these mode frequencies in the crystal, rush replied that, as far as he could ascertain, the observed torsional peak widths at low temperature were very close to the resolution limit. This observation suggests little dispersion of mode frequencies as a result of intermolecular coupling. 

The couplings between the 0H- -0 and -NH2 groups of the 5-amino-tropolone molecule have been of experimental and theoretical interest [52]. In part this is because the -NH2 in the Sq state may be pyramidal, and in the Sj state it may be planar. The 5-hydroxy-tropolone molecule is planar with an asymmetric doubleminimum PES, and part of its interest resides in the possibility of driving the tro-polone tautomerization by laser pumping of the C(5)OH torsion vibration [49, 50,... 

In this expression V x, V and V3 are partition functions for torsional vibration which can be temperature-dependent, 81 S2 and Ss are chemical shifts of the given proton in the three separate rotamers, Ex, Ez and E3 are the energies of the potential maxima from the zero point torsional levels in each separate rotamer. Coupling constants are averaged in a similar way by replacing S in equation (77) by J in order to obtain J averaging. 

The PE spectroscopic evidence for silaethene as the retrodiene dissociation product51 rests on the coincidence between precalculated and observed ionization energies, on the band intensity increase upon addition of argon to the gas stream, which apparently reduces secondary reactions such as oligomerization, and on the vibrational fine structure of the first PES band, which resembles that of the iso(valence)electronic ethene and precludes with high probability the presence of carbene or silylene isomers. Possibly, the silaethene radical cation H2Si=CH 2e possesses a twisted ground-state equilibrium structure like H2C=CH 2 with the two lowest doublet states coupled via the torsional vibration v6 (cf. Reference 10). 

Other cross-coupling terms include bond-torsion and bend-bend-torsion. Cross-coupling terms are important for accurate modeling of normal mode vibrational frequencies and to better model the potential at large deformation (i.e., positions far from the potential minimum). 

An assignment on the basis of a model of coupled torsional vibrations is given by Frank et where the benzene ring,... 

A compact ultrasonic rotory motor, as tiny as 3 mm in diameter, has been developed at the Pennsylvania State University. As shown in Figure 4.1.37, the stator consists of a piezoelectric ring and two concave/convex metal endcaps with windmill shaped slots bonded together, so as to generate a coupling of the up-down and torsional vibrations [60]. Since the number of components is reduced and the fabrication process is much simplified, the fabrication price is decreased remarkably, and a disposable design becomes feasible. When driven at 160 kHz, a maximum revolution of 600 rpm and a maximum torque of 1 mN m were obtained for a 11 mm diameter motor. 

U- and V-shaped TLCGD Plane TLCGD ideal to suppress horizontal and coupled bending torsional vibrations of civil engineering structures. 

We have also studied the overtone induced dissociation of HOOH by classical trajectory calculations using different Hamiltonians (12). Our results illustrate the importance of bending modes and provide evidence for incomplete relaxation of energy. The experimental data suggest a strong coupling of the torsional vibration to the HO stretch mode due to the dependence of the torsional barrier heights on the level of HO excitation, but the trajectory studies are not yet conclusive. The importance of rotation has been stressed by Sumpter and Thompson(12). 

---