Dynamic Analysis of Flexible Rotors Subjected to Torque and Force

1993 ◽  
Author(s):  
Jong-Seop Yun ◽  
Chong-Won Lee
Keyword(s):  
Numerical Analysis ◽  
Variational Principle ◽  
Dynamic Analysis ◽  
Natural Frequency ◽  
Stability Criterion ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Flexible Rotors ◽  
The Stability ◽  
Admissible Functions

Abstract The effect of the applied direction and magnitude of loads on the stability and natural frequency of flexible rotors is analyzed, when the rotors are subject to nonconservative torque and force. The stability criterion derived from the energy and variational principle is discussed and a general Galerkin’s method which utilizes admissible functions is employed for numerical analysis. Illustrative examples are treated to demonstrate the analytical developments.

Application of Galerkin's method to the dynamic analysis of structures.

AIAA Journal ◽  
1967 ◽  
Vol 5 (4) ◽  
pp. 792-795 ◽  
Author(s):  
YI-YUAN YU ◽  
JAI-LUE LAI
Keyword(s):  
Dynamic Analysis ◽  
Galerkin’S Method ◽  
Galerkin's Method

Stability of a Beam on an Elastic Foundation Subjected to a Nonconservative Load

1980 ◽  
Vol 47 (1) ◽  
pp. 116-120 ◽  
Author(s):  
Z. Celep
Keyword(s):  
Approximate Solution ◽  
Numerical Calculation ◽  
Elastic Foundation ◽  
Cantilever Beam ◽  
Numerical Study ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
The Common ◽  
The Stability

In this investigation, the influence of a Winkler type of elastic foundation on the stability of the cantilever beam subjected to a nonconservative load which consists of a vertical and a follower components is studied. In addition to the common transverse foundation modulus, a rotatory foundation modulus is considered. Approximate solution is obtained by using Galerkin’s method. Numerical calculation are reported and displayed for various combinations of the nonconservativeness parameter, transverse and rotatory modulus of the foundation, distance of the point of application of the load and that of the transverse spring. As a result of the numerical study unexpected feature of stability of the cantilever beam in contrast to the behavior of the column is identified.

scholarly journals The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method

2019 ◽  
Vol 19 (3) ◽  
pp. 503-522 ◽  
Author(s):  
Paul Houston ◽  
Ignacio Muga ◽  
Sarah Roggendorf ◽  
Kristoffer G. van der Zee
Keyword(s):  
Direct Proof ◽  
Diffusion Reaction ◽  
Stability And Convergence ◽  
Well Posedness ◽  
Reaction Equation ◽  
Galerkin’S Method ◽  
Convection Diffusion ◽  
Galerkin's Method ◽  
The Stability ◽  
Functional Setting

AbstractWhile it is classical to consider the solution of the convection-diffusion-reaction equation in the Hilbert space {H_{0}^{1}(\Omega)}, the Banach Sobolev space {W^{1,q}_{0}(\Omega)}, {1<q<{\infty}}, is more general allowing more irregular solutions. In this paper we present a well-posedness theory for the convection-diffusion-reaction equation in the {W^{1,q}_{0}(\Omega)}-{W_{0}^{1,q^{\prime}}(\Omega)} functional setting, {\frac{1}{q}+\frac{1}{q^{\prime}}=1}. The theory is based on directly establishing the inf-sup conditions. Apart from a standard assumption on the advection and reaction coefficients, the other key assumption pertains to a subtle regularity requirement for the standard Laplacian. An elementary consequence of the well-posedness theory is the stability and convergence of Galerkin’s method in this setting, for a diffusion-dominated case and under the assumption of {W^{1,q^{\prime}}}-stability of the {H_{0}^{1}}-projector.

On Schwarzschild's Stability Criterion

1971 ◽  
Vol 26 (12) ◽  
pp. 1992-1994 ◽  
Author(s):  
Dietrich Lortz
Keyword(s):  
Gravitational Field ◽  
Variational Principle ◽  
Stability Criterion ◽  
Initial Conditions ◽  
Quadratic Mean ◽  
External Gravitational Field ◽  
The Stability ◽  
Linear Disturbance ◽  
Necessary And Sufficient ◽  
Entropy Criterion

The stability of a gas in an external gravitational field Φ is investigated for arbitrary initial conditions. It is shown that Schwarzschild's entropy criterion ds/dΦ > 0 is both necessary and sufficient for the spatial quadratic mean of a linear disturbance to be bounded in time. The variational principle usually applied is not always sufficient for stability

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

Galerkin’s method revisited and corrected in the problem of Jaworski and Dowell

2021 ◽  
Vol 155 ◽  
pp. 107604
Author(s):  
Isaac Elishakoff ◽  
Marco Amato ◽  
Alessandro Marzani
Keyword(s):  
Galerkin’S Method ◽  
Galerkin's Method

Intrinsic Thermal Stability of Anisotropic Thin-Film Superconductors

1990 ◽  
Vol 112 (1) ◽  
pp. 10-15 ◽  
Author(s):  
M. I. Flik ◽  
C. L. Tien
Keyword(s):  
Thin Film ◽  
Thermal Stability ◽  
Stability Criterion ◽  
High Temperature Superconductors ◽  
Stability Criteria ◽  
Anisotropic Thermal Conductivity ◽  
Operating Current ◽  
Released Energy ◽  
The Stability ◽  
Thermal Stability Of

Intrinsic thermal stability denotes a situation where a superconductor can carry the operating current without resistance at all times after the occurrence of a localized release of thermal energy. This novel stability criterion is different from the cryogenic stability criteria for magnets and has particular relevance to thin-film superconductors. Crystals of ceramic high-temperature superconductors are likely to exhibit anisotropic thermal conductivity. The resultant anisotropy of highly oriented films of superconductors greatly influences their thermal stability. This work presents an analysis for the maximum operating current density that ensures intrinsic stability. The stability criterion depends on the amount of released energy, the Biot number, the aspect ratio, and the ratio of the thermal conductivities in the plane of the film and normal to it.

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