scholarly journals On Curve Veering and Flutter of Rotating Blades

1994 ◽  
Vol 116 (3) ◽  
pp. 702-708 ◽  
Author(s):  
D. Afolabi ◽  
O. Mehmed
Keyword(s):  
Algebraic Geometry ◽  
Catastrophe Theory ◽  
Algebraic Curves ◽  
Rotation Speed ◽  
Elastic Stability ◽  
Rotating Blades ◽  
Rotating Blade ◽  
Modes Of Vibration ◽  
Curve Veering ◽  
As If

The eigenvalues of rotating blades usually change with rotation speed according to the Stodola-Southwell criterion. Under certain circumstances, the loci of eigenvalues belonging to two distinct modes of vibration approach each other very closely, and it may appear as if the loci cross each other. However, our study indicates that the observable frequency loci of an undamped rotating blade do not cross, but must either repel each other (leading to “curve veering”), or attract each other (leading to “frequency coalescence”). Our results are reached by using standard arguments from algebraic geometry—the theory of algebraic curves and catastrophe theory. We conclude that it is important to resolve an apparent crossing of eigenvalue loci into either a frequency coalescence or a curve veering, because frequency coalescence is dangerous since it leads to flutter, whereas curve veering does not precipitate flutter and is, therefore, harmless with respect to elastic stability.

scholarly journals On Curve Veering and Flutter of Rotating Blades

1993 ◽  
Author(s):  
Daré Afolabi ◽  
Oral Mehmed
Keyword(s):  
Algebraic Geometry ◽  
Catastrophe Theory ◽  
Algebraic Curves ◽  
Rotation Speed ◽  
Elastic Stability ◽  
Rotating Blades ◽  
Rotating Blade ◽  
Modes Of Vibration ◽  
Curve Veering ◽  
As If

The eigenvalues of rotating blades usually change with rotation speed according to the Stodola-Southwell criterion. Under certain circumstances, the loci of eigenvalues belonging to two distinct modes of vibration approach each other very closely, and it may appear as if the loci cross each other. However, our study indicates that the observable frequency loci of an undamped rotating blade do not cross, but must either repel each other (leading to “curve veering”), or attract each other (leading to “frequency coalescence”). Our results are reached by using standard arguments from algebraic geometry — the theory of algebraic curves and catastrophe theory. We conclude that it is important to resolve an apparent crossing of eigenvalue loci into either a frequency coalescence or a curve veering, because frequency coalescence is dangerous since it leads to flutter, whereas curve veering does not precipitate flutter and is, therefore, harmless with respect to elastic stability.

scholarly journals Injective linear series of algebraic curves on quadrics

2020 ◽  
Vol 66 (2) ◽  
pp. 231-254
Author(s):  
Edoardo Ballico ◽  
Emanuele Ventura
Keyword(s):  
Algebraic Geometry ◽  
Projective Space ◽  
Algebraic Curves ◽  
Linear Series ◽  
Central Importance ◽  
Arbitrary Characteristic ◽  
Space Curves

Abstract We study linear series on curves inducing injective morphisms to projective space, using zero-dimensional schemes and cohomological vanishings. Albeit projections of curves and their singularities are of central importance in algebraic geometry, basic problems still remain unsolved. In this note, we study cuspidal projections of space curves lying on irreducible quadrics (in arbitrary characteristic).

Effects of Free Damping Layers on Harmonic Response of Rotating Blades

1989 ◽  
Author(s):  
T. H. Young ◽  
T. N. Shiau ◽  
S. H. Chiu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Modulus ◽  
Loss Factor ◽  
Harmonic Excitation ◽  
The Finite Element Method ◽  
Harmonic Response ◽  
Rotating Blades ◽  
Rotating Blade ◽  
Triangular Elements

This paper studies the forced vibration of a rotating blade with free damping layers to harmonic excitation by means of the finite element method. The damping layers are made of viscoelastic material with complex elastic modulus, and the excitation may be either distributed or concentrated. Triangular elements with totally 15 d.o.f. are used to allow for a great variety of shapes and boundary conditions. The effects of various parameters, such as loss factor, storage modulus and thickness of damping layers, are investigated. The results show that the vibration amplitudes near resonances can be significantly reduced by the free damping layers.

scholarly journals ALGEBRAIC GEOMETRY AND HOFSTADTER TYPE MODEL

2002 ◽  
Vol 16 (14n15) ◽  
pp. 2097-2106
Author(s):  
SHAO-SHIUNG LIN ◽  
SHI-SHYR ROAN
Keyword(s):  
Algebraic Geometry ◽  
Physical Model ◽  
Algebraic Curves ◽  
Spectral Curve ◽  
Rational Curves ◽  
Type Model ◽  
Bethe Equation ◽  
Explicit Solutions ◽  
Polynomial Roots ◽  
High Genus

In this report, we study the algebraic geometry aspect of Hofstadter type models through the algebraic Bethe equation. In the diagonalization problem of certain Hofstadter type Hamiltonians, the Bethe equation is constructed by using the Baxter vectors on a high genus spectral curve. When the spectral variables lie on rational curves, we obtain the complete and explicit solutions of the polynomial Bethe equation; the relation with the Bethe ansatz of polynomial roots is discussed. Certain algebraic geometry properties of Bethe equation on the high genus algebraic curves are discussed in cooperation with the consideration of the physical model.

Study on Vibration Characteristics of High-Speed Rotating Constrained Blades Based on Spin Softening

2017 ◽  
Vol 863 ◽  
pp. 241-245
Author(s):  
Hui Ying Zhao ◽  
Xiu Hua Men
Keyword(s):  
Dynamic Model ◽  
Mode Shape ◽  
High Speed ◽  
Engineering Application ◽  
Rotor Dynamics ◽  
Vibration Characteristics ◽  
Blade Vibration ◽  
Rotating Blades ◽  
Rotating Blade ◽  
Optimal Designing

Based on the theories of rotor dynamics, a dynamic model of rotating blade was built. Taking account of the effect of spin softening, the research on vibration characteristics of high-speed rotating blades was carried out under different speeds. The results had shown that frequency of blade vibration increased with rising rotating velocity, whilst the frequency of all orders declined with the influence of spin softening. Meanwhile, the change of each mode shape of blade was not very large at different speed. The conclusion derived from this paper had both theoretical and empirical value on retrofitting, optimal-designing, as well as engineering application for high-speed rotating blades.

MODIFIKASI DESAIN TRAKTOR TANGAN “TEMBESI” (STUDI KASUS DI PERKEBUNAN “TEMBESI”)

SIGMA TEKNIKA ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
Agus Supono ◽  
Agus Umar Ryadin ◽  
Fadhlem Bassar Minta
Keyword(s):  
Rotation Speed ◽  
Motor Power ◽  
Design Modification ◽  
Rotating Blade ◽  
Rubber Tire ◽  
Blade Rotation ◽  
Previous Design ◽  
The Moment

"Tembesi" hand tractor is a tool in the field of agriculture that is used to loosen the soil that is driven by gasoline fuel motor with a driving motor power of 6.5 Hp. From the results of the previous design testing (Rev_00) found a problem, where the tractor is difficult to move and when the rotating blade is then given a load the blade stops rotating. This study aims to improve the design of the "Tembesi" hand tractor which is focused on reducing the number of blade turns to increase the moment value and repair the part of the tractor wheel.From the design modification results, the blade rotation speed is modified from 1333 rpm to 450 rpm. From the plan moment value 6,925 kg.mm, the force produced by the "Tembesi" hand tractor blade is 387,79 Newton. Wheel modification is carried out using a 12-inch diameter (304.8 mm) rubber tire wheel.

A comparison between Suzuki invariant code and one-point Hermitian code

2021 ◽  
pp. 2150104
Author(s):  
Abdulla Eid
Keyword(s):  
Algebraic Geometry ◽  
Minimum Distance ◽  
Algebraic Curves ◽  
Automorphism Groups ◽  
Algebraic Geometry Codes ◽  
Hermitian Codes ◽  
Relative Minimum ◽  
Minimum Distances ◽  
Hermitian Code

In this paper we compare the performance of two algebraic geometry codes (Suzuki and Hermitian codes) constructed using maximal algebraic curves over [Formula: see text] with large automorphism groups by choosing specific divisors. We discuss their parameters, compare the rate of these codes as well as their relative minimum distances, and we show that both codes are asymptotically good in terms of the rate which is in contrast to their behavior in terms of the relative minimum distance.

scholarly journals Residually finite rationally p groups

2019 ◽  
Vol 22 (03) ◽  
pp. 1950016
Author(s):  
Thomas Koberda ◽  
Alexander I. Suciu
Keyword(s):  
Algebraic Geometry ◽  
Group Theory ◽  
Large Class ◽  
Algebraic Curves ◽  
Fundamental Groups ◽  
Finitely Generated ◽  
Residual Property ◽  
Residually Finite ◽  
Torsion Freeness ◽  
Do So

In this paper, we develop the theory of residually finite rationally [Formula: see text] (RFR[Formula: see text]) groups, where [Formula: see text] is a prime. We first prove a series of results about the structure of finitely generated RFR[Formula: see text] groups (either for a single prime [Formula: see text], or for infinitely many primes), including torsion-freeness, a Tits alternative, and a restriction on the BNS invariant. Furthermore, we show that many groups which occur naturally in group theory, algebraic geometry, and in 3-manifold topology enjoy this residual property. We then prove a combination theorem for RFR[Formula: see text] groups, which we use to study the boundary manifolds of algebraic curves [Formula: see text] and in [Formula: see text]. We show that boundary manifolds of a large class of curves in [Formula: see text] (which includes all line arrangements) have RFR[Formula: see text] fundamental groups, whereas boundary manifolds of curves in [Formula: see text] may fail to do so.

Imperfection-sensitivity of semi-symmetric branching

1977 ◽  
Vol 357 (1689) ◽  
pp. 193-211 ◽  
Keyword(s):  
General Theory ◽  
Potential Function ◽  
Catastrophe Theory ◽  
Bifurcation Theory ◽  
Elastic Stability ◽  
Structural Systems ◽  
Stiffened Plate ◽  
Imperfection Sensitivity ◽  
Branching Points ◽  
Symmetric Points

The general theory of elastic stability is extended to include the imperfection-sensitivity of twofold compound branching points with symmetry of the potential function in one of the critical modes (semi-symmetric points of bifurcation). Three very different forms of imperfection-sensitivity can result, so a subclassification into monoclinal, anticlinal and homeoclinal semi-symmetric branching is introduced. Relating this bifurcation theory to René Thom’s catastrophe theory, it is found that the anticlinal point of bifurcation generates an elliptic umbilic catastrophe, while the monoclinal and homeoclinal points of bifurcation lead to differing forms of the hyperbolic umbilic catastrophe. Practical structural systems which can exhibit this form of branching include an optimum stiffened plate with free edges loaded longitudinally, and an analysis of this problem is presented leading to a complete description of the imperfection-sensitivity. The paper concludes with some general remarks concerning the nature of the optimization process in design as a generator of symmetries, instabilities and possible compound bifurcations.

scholarly journals Numerical Simulation and Experimental Investigation of Rotating Blade Centrifugal Jet in Slurry Blast Device Used for Steel Strip Descaling

2022 ◽  
Vol 12 (1) ◽  
pp. 478
Author(s):  
Guotao Huo ◽  
Zhonghai Ma ◽  
Yeqing Huang ◽  
Songlin Nie ◽  
Zhenhua Zhang
Keyword(s):  
Numerical Simulation ◽  
Erosion Rate ◽  
Rotation Speed ◽  
Steel Strip ◽  
Experimental System ◽  
Inlet Pressure ◽  
Rotating Blade ◽  
Steel Strips ◽  
Simulation Results ◽  
Low Efficiency

Under the requirement of clean production, a new type of slurry blast device for mechanically removing oxide scale on the surface of steel strips is presented, which can avoid the serious problems of rapid wear, low service life, and low efficiency of the traditional abrasive water jet with a nozzle. In this paper, the numerical simulation of the rotating blade centrifugal jet in the slurry blast device is conducted based on CFD, where the DPM and the erosion model are innovatively employed to simulate the movement characteristics of abrasive particles and the erosion rate of mixed slurry on the surface of the steel strip. Simulation results show that the erosion rate and particle motion velocity are proportional to the blade rotation speed and inlet pressure. Reasonable inlet pressure and rotation speed are helpful for improving the rust removal efficiency of slurry blast devices. An experimental system is established to validate the simulation results. The experimental results are consistent with the simulation trend, which exhibits that the developed slurry blast device is feasible for steel strip descaling. This work will play substantial guiding roles in the engineering optimization of slurry blast devices for steel strip descaling.

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