The application of the matrix method of successive approximations to the calculation of the force constants of tetramethylmethane

1971 ◽  
Vol 14 (7) ◽  
pp. 918-921
Author(s):  
N. F. Kovalenko ◽  
V. P. Morozov
Keyword(s):  
Matrix Method ◽  
Force Constants ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
The Matrix

Determination of the Force Constants of Non-linear XY2 Molecules in the Gas-Phase by the GF Matrix Method

2004 ◽  
Vol 59 (9) ◽  
pp. 621-622 ◽  
Author(s):  
Fatih Ucun ◽  
Vesile Gūçlü
Keyword(s):  
Gas Phase ◽  
Condensed Phase ◽  
Matrix Method ◽  
Solid Phase ◽  
Force Constants ◽  
Matrix Solution ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of nonlinear XY2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.

Determination of Force Constants of Planar XY3 and Tetrahedral XY4 Molecules by the GF Matrix Method

2005 ◽  
Vol 60 (3) ◽  
pp. 183-186 ◽  
Author(s):  
Vesile Güçlü ◽  
Fatih Ucun
Keyword(s):  
Computer Program ◽  
Matrix Method ◽  
Force Constants ◽  
Internal Coordinates ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of planar XY3 and tetrahedral XY4 molecules were calculated using the GF matrix method. The matrix solutions were carried out by means of a computer program built relative to the Newton-Raphson method, and the calculations were listed in tables. For tetrahedral XY4 molecules having the same Y atom it was found that the force constants decrease with the increasing mass of the X atom, and this was attributed to the slowing of the molecule with increasing mass of the centre X atom.

Determination of Force Constants of Octahedral XY6 Molecules by the GF Matrix Method

2005 ◽  
Vol 60 (11-12) ◽  
pp. 819-822 ◽  
Author(s):  
Fatih Ucun ◽  
M. Gökhan Şengül
Keyword(s):  
Matrix Method ◽  
Molar Mass ◽  
Interaction Force ◽  
Force Constants ◽  
Complex Ions ◽  
Slowing Down ◽  
The Matrix ◽  
The Difference ◽  
Raphson Method

The force constants of the internal coordinates of octahedral XY6 molecules and complex ions were calculated by using the GF matrix method. The matrix solutions were found by means of a computer program using the Newton-Raphson method. From the calculations it has been observed that the bond stretch force constants of octahedral XF6 molecules and XY6 complex ions having the same centre X atom decrease with the increasing molar mass of the centre X atom for the former and the ligand Y atom for the latter, respectively. This was attributed to the slowing down of the molecule with increasing molar mass of the molecule as the whole. In addition we have concluded that the difference of squares of the vibration frequencies ν1 and ν2 of octahedral XY6 complex ions decreases with the increasing mass of the Y atom since the interaction force constant of these ions decreases with the increasing mass.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

scholarly journals Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions

2015 ◽  
Vol 20 (4) ◽  
pp. 939-951
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
The Core ◽  
Analytical Frequency

Abstract Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.

Molecular Force Fields of Some Selenium and Telurium Hexahalide Ions

1970 ◽  
Vol 25 (4) ◽  
pp. 566-569
Author(s):  
M. N. Avasthi ◽  
M. L. Mehta
Keyword(s):  
Matrix Method ◽  
Force Fields ◽  
Force Constants ◽  
Mean Amplitudes Of Vibration ◽  
Molecular Force

Abstract Wilson's GF matrix method has been used to evaluate all the seven independent force constants of some XY6 type ions using Müller's mathematical constraint. Mean amplitudes of vibration and Bastiansen-Morino shrinkages have also been calculated for these ions.

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