The Dynamically Loaded Circular Beam on an Elastic Foundation

1980 ◽  
Vol 47 (1) ◽  
pp. 139-144 ◽  
Author(s):  
D. E. Panayotounakos ◽  
P. S. Theocaris
Keyword(s):  
Elastic Foundation ◽  
Discrete System ◽  
Natural Frequencies ◽  
Continuous System ◽  
Rotatory Inertia ◽  
Analytical Treatment ◽  
Linear Partial Differential Equations ◽  
Circular Beam ◽  
Solution Methodology

In this investigation an analytical treatment for the determination of the natural frequencies of a circular uniform beam on an elastic foundation, subjected to harmonic loads, is presented. This problem in the most general case of response is reduced to a system of six-coupled linear partial differential equations. The effects of rotatory inertia and transverse shear deformation are also included in the analysis. The problem is treated by considering the beam as a continuous system, as well as a discrete system. The aforementioned solution methodology is successfully demonstrated through several numerical examples.

Three-Dimensional Harmonic Vibrations of a Circular Beam

1984 ◽  
Vol 51 (2) ◽  
pp. 375-382 ◽  
Author(s):  
D. E. Panayotounakos ◽  
P. S. Theocaris
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Analytical Treatment ◽  
Six Degrees Of Freedom ◽  
Harmonic Vibrations ◽  
Differential Element ◽  
Circular Beam ◽  
Partial Linear ◽  
Linear Differential

In this paper an analytical treatment for the determination of the natural frequencies of a circular uniform beam, subjected to three-dimensional harmonic loads, is presented. Each differential element of the beam has six degrees of freedom, i.e., three translations and three rotations. This problem, in the most general case of response, is associated with a partial linear differential system composed of four coupled 3 × 1 vectorial equations. The influences of transverse shear deformation and rotatory inertia are also included in the analysis. The aforementioned solution methodology is successfully demonstrated through several numerical results.

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.

CHARACTERIZATION OF NUCLEAR IMAGES BASED ON ANALYSIS OF FRACTIONAL SUMMATION SYSTEMS

Fractals ◽  
2004 ◽  
Vol 12 (02) ◽  
pp. 157-169 ◽  
Author(s):  
HAI-SHAN WU ◽  
ANDREW J. EINSTEIN ◽  
LIANE DELIGDISCH ◽  
TAMARA KALIR ◽  
JOAN GIL
Keyword(s):  
White Noise ◽  
Frequency Domain ◽  
Discrete System ◽  
Fractional Integral ◽  
Continuous System ◽  
Time Range ◽  
System Function ◽  
Autocovariance Function ◽  
Frequency Domain Methods

While frequency-based methods for the characterization of fractals are popular and effective in many applications, they have limitations when applied to irregularly shaped images, such as nuclear images. The irregularity renders texture characterization by frequency domain methods, based upon Fourier transform, problematic. To address this situation, this paper presents an algorithm based upon the signal analysis in the spatial domain. An autocovariance function can be estimated regardless of the shape and size of regions where the image is defined. As in the continuous fractional Brownian motion (FBM) that results from inputting white noise into a specific fractional integral system, a discrete FBM can be related to white noise by a specific fractional summation system (FSS) that is linear, causal and shift-invariant. Although the method of direct sampling is not valid for converting a continuous fractional integral to a discrete fractional summation, discrete fractional summations similar to the sampled system functions can be obtained through an iterative process. While the continuous system function of a fractional integral is linear in the frequency domain when plotted in log-log scales, unfortunately, it is not true for the comparable discrete system function. The discrete system function is actually approximately linear in the log-log scales over a very limited range. The slope of the straight line that approximates the function curve in the mean-square-error (MSE) sense in a specific time range provides a description of the autocovariance function that reveals the statistical relations among the local textures. Applications to characterization of ovary nuclear images in groups of normal, atypical and cancer cases are studied and presented.

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