DISPERSION RELATIONS FOR PHONONS IN MAGNESIUM FLUORIDE

1967 ◽  
Vol 45 (9) ◽  
pp. 3079-3090 ◽  
Author(s):  
R. S. Katiyar ◽  
R. S. Krishnan
Keyword(s):  
Secular Equation ◽  
Normal Modes ◽  
Theoretical Method ◽  
Dispersion Relations ◽  
Magnesium Fluoride ◽  
Ionic Character ◽  
Axially Symmetric ◽  
Longitudinal Modes ◽  
Modes Of Vibration ◽  
Crystallographic Axes

The lattice dynamics of magnesium fluoride have been investigated theoretically. The group theoretical method is used to decompose the dynamical secular equation at the center of the Brillouin zone. In order to get the expressions for all the infrared-active transverse and longitudinal modes, it is necessary to decompose the secular equation for the wave vector approaching zero along the two nonequivalent crystallographic axes, say y and z, of the crystal. Analysis of the results shows that a rigid ion model of the crystal with axially symmetric forces can provide qualitative agreement with the observed frequencies appearing in Raman and infrared absorption. The ions in the crystal are found to retain 70% of their charges, showing thereby the ionic character of the crystal. The dispersion relations for normal modes of vibration propagating along the (0 0 qz) and (0 qy 0) directions have been evaluated.

scholarly journals Preparation and the Microwave and Infrared Spectra of Vinyl Ketene

1979 ◽  
Vol 34 (11) ◽  
pp. 1269-1274 ◽  
Author(s):  
Erik Bjarnov
Keyword(s):  
Dipole Moment ◽  
Gas Phase ◽  
Infrared Spectra ◽  
Room Temperature ◽  
Normal Modes ◽  
Spectroscopic Constants ◽  
Electrical Dipole ◽  
Electrical Dipole Moment ◽  
Vacuum Pyrolysis ◽  
Modes Of Vibration

Vinyl ketene (1,3-butadiene-1-one) has been synthesized by vacuum pyrolysis of 3-butenoic 2-butenoic anhydride. The microwave and infrared spectra of vinyl ketene in the gas phase at room temperature have been studied. The trans-rotamer has been identified, and the spectroscopic constants were found to be Ã= 39571(48) MHz, B̃ = 2392.9252(28) MHz, C̃ = 2256.0089(28) MHz, ⊿j = 0.414(31) kHz, and ⊿JK = - 34.694(92) kHz. The electrical dipole moment was found to be 0.987(23) D with μa = 0.865(14) D and μb = 0.475(41) D. A tentative assignment has been made for 17 of the 21 normal modes of vibration

Normal modes of vibration of a model peptide adopting the C7 C5 structure

2009 ◽  
Vol 24 (6) ◽  
pp. 543-552 ◽  
Author(s):  
P. LAGANT ◽  
G. VERGOTEN ◽  
G. FLEURY ◽  
M.H. LOUCHEUX-LEFEBVRE
Keyword(s):  
Normal Modes ◽  
Model Peptide ◽  
Modes Of Vibration

Vibration of Rectangular Plates by the Ritz Method

1950 ◽  
Vol 17 (4) ◽  
pp. 448-453 ◽  
Author(s):  
Dana Young
Keyword(s):  
Ritz Method ◽  
Normal Modes ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Modes Of Vibration ◽  
Ritz’S Method ◽  
Square Plate ◽  
Set Up

Abstract Ritz’s method is one of several possible procedures for obtaining approximate solutions for the frequencies and modes of vibration of thin elastic plates. The accuracy of the results and the practicability of the computations depend to a great extent upon the set of functions that is chosen to represent the plate deflection. In this investigation, use is made of the functions which define the normal modes of vibration of a uniform beam. Tables of values of these functions have been computed as well as values of different integrals of the functions and their derivatives. With the aid of these data, the necessary equations can be set up and solved with reasonable effort. Solutions are obtained for three specific plate problems, namely, (a) square plate clamped at all four edges, (b) square plate clamped along two adjacent edges and free along the other two edges, and (c) square plate clamped along one edge and free along the other three edges.

Localization of Vibration in Disordered Multi-Span Beams With Damping

1993 ◽  
Author(s):  
Djamel Bouzit ◽  
Christophe Pierre
Keyword(s):  
Weak Coupling ◽  
Normal Modes ◽  
Structural Damping ◽  
Coupling Case ◽  
Effects Of Disorder ◽  
Transfer Matrix Approach ◽  
Modes Of Vibration ◽  
Comparable Magnitude ◽  
Localization Of Vibration ◽  
Statistical Perturbation

Abstract The combined effects of disorder and structural damping on the dynamics of a multi-span beam with slight randomness in the spacing between supports are investigated. A wave transfer matrix approach is chosen to calculate the free and forced harmonic responses of this nearly periodic structure. It is shown that both harmonic waves and normal modes of vibration that extend throughout the ordered, undamped beam become spatially attenuated if either small damping or small disorder is present in the system. The physical mechanism which causes this attenuation, however, is one of energy dissipation in the case of damping but one of energy confinement in the case of disorder. The corresponding rates of spatial exponential decay are estimated by applying statistical perturbation methods. It is found that the effects of damping and disorder simply superpose for a multi-span beam with strong interspan coupling, but interact less trivially in the weak coupling case. Furthermore, the effect of disorder is found to be small relative to that of damping in the case of strong interspan coupling, but of comparable magnitude for weak coupling between spans. The adequacy of the statistical analysis to predict accurately localization in finite disordered beams with boundary conditions is also examined.

scholarly journals Normal modes of a "cylindrical valley" of alluvium

1989 ◽  
Vol 22 (2) ◽  
pp. 76-80 ◽  
Author(s):  
W. R. Stephenson
Keyword(s):  
Shear Modulus ◽  
Structural Damage ◽  
Travelling Waves ◽  
Soft Soil ◽  
Normal Modes ◽  
Modes Of Vibration ◽  
Rigid Material ◽  
Cylindrical Volume ◽  
High Bulk ◽  
Low Shear

Some normal modes of vibration are deduced for a cylindrical volume of high bulk modulus, low shear modulus material, embedded in an infinite half space of rigid material. The manner in which they may be excited by travelling waves in the rigid material is examined. The relevance of such processes is discussed with regard to the enhancement of structural damage on soft soil during an earthquake.

The effect of fast-time-scale turbulence on magnetohydrodynamical behaviour

1984 ◽  
Vol 31 (1) ◽  
pp. 81-92 ◽  
Author(s):  
R. O. Dendy ◽  
D. Ter Haar
Keyword(s):  
Time Scale ◽  
Normal Modes ◽  
Dispersion Relations ◽  
Magnetized Plasma ◽  
Fast Time ◽  
Fast Time Scale ◽  
Scale Turbulence ◽  
The Ideal

We show what corrections have to be made to the equations of ideal magneto-hydrodynamics when there is fast-time-scale turbulence present in a magnetized plasma. We show how the dispersion relations for the ideal Alfvén and magnetoacoustic MHD normal modes are modified when such turbulence is present. Finally, we discuss the relation of our work to that of other authors.

Relation between creeping waves and normal modes of vibration of a curved body

1977 ◽  
Vol 61 (3) ◽  
pp. 711-715 ◽  
Author(s):  
H. Überall ◽  
L. R. Dragonette ◽  
L. Flax
Keyword(s):  
Normal Modes ◽  
Modes Of Vibration
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