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.

Numerical study of the magnetohydrodynamic spectra in tokamaks using galerkin's method

1975 ◽  
Vol 18 (2) ◽  
pp. 132-153 ◽  
Author(s):  
R.L. Dewar ◽  
J.M. Greene ◽  
R.C. Grimm ◽  
J.L. Johnson
Keyword(s):  
Numerical Study ◽  
Galerkin’S Method ◽  
Galerkin's Method

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.

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.

scholarly journals The Approximated Solution for The Nonlinear Second Order Delay Multi-Value Problems

2011 ◽  
Vol 8 (1) ◽  
pp. 175-178
Author(s):  
Baghdad Science Journal
Keyword(s):  
Approximate Solution ◽  
Second Order ◽  
Galerkin’S Method ◽  
Galerkin's Method

This paper is attempt to study the nonlinear second order delay multi-value problems. We want to say that the properties of such kind of problems are the same as the properties of those with out delay just more technically involved. Our results discuss several known properties, introduce some notations and definitions. We also give an approximate solution to the coined problems using the Galerkin's method.

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