Determination of the natural frequencies and mode shapes for large structures by accelerated Newton-Raphson method

1997 ◽  
Vol 63 (1) ◽  
pp. 61-68 ◽  
Author(s):  
In-Won Lee ◽  
Man-Cheol Kim ◽  
A.R. Robinson
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Large Structures ◽  
Newton Raphson ◽  
Raphson Method

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.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

Determination of the first n modes of a tall building from a reduced eigenvalue problem

1964 ◽  
Vol 54 (4) ◽  
pp. 1233-1254
Author(s):  
Moshe F. Rubinstein
Keyword(s):  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Tall Building ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Story Building

Abstract The first n natural frequencies and mode shapes of an N degree of freedom structure (n < N) are derived from the solution of a reduced eigenvalue problem of order smaller than N. The reduced eigenvalue problem is formulated by using experience to select approximations to the first n modes desired. Accuracy is improved when more than n modes are selected. The method is illustrated by a study on an 18 story building.

An Extension of the Holzer Method for Redundant Drive Trains

1974 ◽  
Vol 96 (2) ◽  
pp. 697-698 ◽  
Author(s):  
M. S. Hundal
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
System Of Equations ◽  
Redundant System ◽  
Drive Trains ◽  
Redundant Drive

A method is described for the determination of natural frequencies and mode shapes of closed drive trains. It is an extension of the Holzer method to a redundant system. The “error” for a given value of frequency is computed by the solution of a tridiagonal system of equations.

scholarly journals On the determination of natural frequencies and mode shapes of cable-stayed bridges

2001 ◽  
Vol 25 (12) ◽  
pp. 1099-1115 ◽  
Author(s):  
F.T.K. Au ◽  
Y.S. Cheng ◽  
Y.K. Cheung ◽  
D.Y. Zheng
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Cable Stayed Bridges

scholarly journals Direct Method for the Determination of Coefficients of Characteristic Equation of a MDOF System

2019 ◽  
Vol 15 (2) ◽  
pp. 26-31
Author(s):  
Mahesh Chandra Luintel
Keyword(s):  
Characteristic Equation ◽  
Natural Frequencies ◽  
Direct Method ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Vibratory System ◽  
Single Degree Of Freedom ◽  
Dynamic Matrix ◽  
Eigen Values

Dynamic response of any single degree of freedom (SDOF) vibratory system is studied by evaluating its natural frequencies whereas that of any multi degree of freedom (MDOF) vibratory system is studied by evaluating its natural frequencies and corresponding mode shapes. Efficient method to determine the natural frequencies and mode shape of a MDOF system is to determine its dynamic matrix and to calculate its eigen-values and eigen-vectors. As the number of degree of freedom (DOF) of the system increases, the size of the dynamic matrix increases and the use of a computer program or package become essential. Hence this paper proposes a new method to directly calculate the coefficients of characteristic equation of any degree of freedom system from which eigen-values and then natural frequencies can be determined.  

Determination of AGMA Geometry Factor J for Slotted External Spur Gears

1983 ◽  
Vol 105 (3) ◽  
pp. 305-311
Author(s):  
Y. P. Singh
Keyword(s):  
Direct Method ◽  
Mining Industry ◽  
Spur Gears ◽  
Input Output ◽  
Typical Application ◽  
Geometry Factor ◽  
Newton Raphson ◽  
A Direct Method ◽  
Raphson Method

This paper presents a direct method for determining the geometry factor J for slotted external spur gears. The location of maximum stressed point on the tooth profile where the stress parabola is tangent to the fillet curve has been determined by solving the resulting nonlinear equations using the sophisticated Newton-Raphson method. The semi-graphical procedure given in AGMA Standard [1] is not convenient for determining the geometry factory J of large gears used in grinding mill and kiln drives in the mining industry. Listing of the computer program and input-output point out for a typical application are presented.

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