4.1.1.3.2 Dynamical matrix and normal modes of vibration

2005 ◽  
pp. 436-438
Author(s):  
R. F. Wallis ◽  
S. Y. Tong
Keyword(s):  
Normal Modes ◽  
Dynamical Matrix ◽  
Modes Of Vibration

Symmetry properties of the normal modes of vibration of calcite and α-corundum

1969 ◽  
Vol 47 (13) ◽  
pp. 1381-1391 ◽  
Author(s):  
E. R. Cowley
Keyword(s):  
Theoretical Analysis ◽  
Normal Modes ◽  
Dispersion Curves ◽  
Dynamical Matrix ◽  
Space Group ◽  
Symmetry Properties ◽  
Modes Of Vibration ◽  
Symmetry Species ◽  
Group Theoretical Analysis

A group theoretical analysis is carried out on the symmetry properties of the normal modes of vibration of crystals with the calcite and α-corundum structures. Both of these structures have the space group [Formula: see text]. The symmetry species present in the dispersion curves are determined for important wave vectors, and a transformation to block-diagonalize the dynamical matrix at the zone center is given.

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

scholarly journals Magnetic Normal Mode Calculations in Big Systems: A Highly Scalable Dynamical Matrix Approach Applied to a Fibonacci-Distorted Artificial Spin Ice

2021 ◽  
Vol 7 (3) ◽  
pp. 34
Author(s):  
Loris Giovannini ◽  
Barry W. Farmer ◽  
Justin S. Woods ◽  
Ali Frotanpour ◽  
Lance E. De Long ◽  
...  
Keyword(s):  
Normal Modes ◽  
Low Frequency ◽  
Fibonacci Sequence ◽  
Exchange Interactions ◽  
Geometric Distortion ◽  
Dynamical Matrix ◽  
Spin Ice ◽  
Magnetization Dynamics ◽  
Distortion Parameter ◽  
Artificial Spin Ice

We present a new formulation of the dynamical matrix method for computing the magnetic normal modes of a large system, resulting in a highly scalable approach. The motion equation, which takes into account external field, dipolar and ferromagnetic exchange interactions, is rewritten in the form of a generalized eigenvalue problem without any additional approximation. For its numerical implementation several solvers have been explored, along with preconditioning methods. This reformulation was conceived to extend the study of magnetization dynamics to a broader class of finer-mesh systems, such as three-dimensional, irregular or defective structures, which in recent times raised the interest among researchers. To test its effectiveness, we applied the method to investigate the magnetization dynamics of a hexagonal artificial spin-ice as a function of a geometric distortion parameter following the Fibonacci sequence. We found several important features characterizing the low frequency spin modes as the geometric distortion is gradually increased.

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

Magnetic normal modes in ferromagnetic nanoparticles: A dynamical matrix approach

2004 ◽  
Vol 70 (5) ◽  
Author(s):  
M. Grimsditch ◽  
L. Giovannini ◽  
F. Montoncello ◽  
F. Nizzoli ◽  
Gary K. Leaf ◽  
...  
Keyword(s):  
Normal Modes ◽  
Dynamical Matrix ◽  
Ferromagnetic Nanoparticles ◽  
Matrix Approach

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.

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