Determination of local inhomogeneity of the medium from the natural frequencies of string oscillations

2018 ◽  
Vol 13 (4) ◽  
pp. 99-106 ◽  
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Power Series ◽  
Natural Frequencies ◽  
Fundamental System ◽  
Quadratic Function ◽  
Local Inhomogeneity ◽  
Conjugation Conditions ◽  
Elastic Characteristics

The paper considers the problem of determining the local inhomogeneity of the medium from the natural frequencies of string oscillation. The inhomogeneity is modeled in three sections: in the first and third sections medium is homogeneous, and on average section the elastic characteristics are modeled by a quadratic function. This model is implemented using the conjugation conditions at boundary between media. It is shown that to identify the center of an inhomogeneity and determine its size, two natural frequencies are enough, and in the case of rigid fixing of both ends of the string, the solution of the problem is dual. The problem is solved by expanding the fundamental system of solutions into a power series in the variables x and λ. The estimates of the error of the method are given.

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

Studies on Determination of Natural Frequencies of Industrial Turbine Blades

1995 ◽  
Author(s):  
Mahesh M. Bhat ◽  
V. Ramamurti ◽  
C. Sujatha
Keyword(s):  
Steam Turbine ◽  
Dynamic Behavior ◽  
Turbine Blade ◽  
Natural Frequencies ◽  
Complex Structure ◽  
Turbine Blades ◽  
Blade Root ◽  
Steam Turbine Blade ◽  
Manufacturing Tolerances

Abstract Steam turbine blade is a very complex structure. It has geometric complexities like variation of twist, taper, width and thickness along its length. Most of the time these variations are not uniform. Apart from these geometric complexities, the blades are coupled by means of lacing wire, lacing rod or shroud. Blades are attached to a flexible disc which contributes to the dynamic behavior of the blade. Root fixity also plays an important role in this behavior. There is a considerable variation in the frequencies of blades of newly assembled turbine and frequencies after some hours of running. Again because of manufacturing tolerances there can be some variation in the blade to blade frequencies. Determination of natural frequencies of the blade is therefore a very critical job. Problems associated with typical industrial turbine bladed discs of a 235 MW steam turbine are highlighted in this paper.

Effect of the Material Types on the Fundamental Frequencies of Uniaxial Composite Conical Springs

1999 ◽  
Author(s):  
Vebil Yildirim ◽  
Erol Sancaktar ◽  
Erhan Kiral
Keyword(s):  
Transfer Matrix Method ◽  
Pitch Angle ◽  
Natural Frequencies ◽  
Axial Deformation ◽  
Helical Springs ◽  
Fundamental Frequencies ◽  
Helix Pitch ◽  
Constant Pitch ◽  
Α Helix

Abstract This paper deals with the effect of the material types (Graphite-Epoxies and Kevlar-Epoxy) on the fundamental frequencies of uniaxial constant-pitch composite conical helical springs with solid circle section and fixed-fixed ends. The transfer matrix method is used for the determination of the fundamental natural frequencies. The rotary inertia, the shear and axial deformation effects are taken into account in the solution. The free vibrational charts for each material presented in this study cover the following vibrational parameters: n (number of active turns) = 5–10, α = (helix pitch angle) = 5° and 25°, R2/R1, (minimum to maximum radii of the cylinder) = 0.1 and 0.9, and Dmax/d (maximum cylinder to wire diameters) = 5 and 15. These charts can be used for the design of uniaxial composite conical springs.

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.

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