A Theoretical Study of the Dynamic Behavior of Foil Bearings

1971 ◽  
Vol 93 (1) ◽  
pp. 133-142 ◽  
Author(s):  
T. B. Barnum ◽  
H. G. Elrod
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Dynamic Behavior ◽  
Theoretical Study ◽  
Compressibility Factor ◽  
Frequency Parameter ◽  
Numerical Results ◽  
Foil Bearings ◽  
Foil Bearing

The differential equations and boundary conditions for the problem of a foil bearing subjected to small variations in tape tension are developed. The numerical results show that the fluctuations of the foil are a function or the frequency parameter ω* = 2r0ωε1/3H0*/U and of the compressibility factor θ = T0/par0.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1991 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Abstract Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

scholarly journals A Comparison between Adomian Decomposition and Tau Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Necdet Bildik ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Tau Method ◽  
Adomian Decomposition

We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.

scholarly journals Thermally Charged MHD Bi-Phase Flow Coatings with Non-Newtonian Nanofluid and Hafnium Particles along Slippery Walls

Coatings ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 300 ◽  
Author(s):  
Rahmat Ellahi ◽  
Ahmed Zeeshan ◽  
Farooq Hussain ◽  
Tehseen Abbas
Keyword(s):  
Magnetic Susceptibility ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Couple Stress ◽  
Numerical Results ◽  
Phase Flow ◽  
Metallic Particles ◽  
Coupled Partial Differential Equations ◽  
Physical Quantities ◽  
Graphical Illustration

The present study is about the pressure-driven heated bi-phase flow in two slippery walls. The non-Newtonian couple stress fluid is suspended with spherically homogenous metallic particles. The magnetic susceptibility of Hafnium allures is taken into account. The rough surface of the wall is tackled by lubrication effects. The nonlinear coupled partial differential equations along with the associated boundary conditions are first reduced into a set of ordinary differential equations by using appropriate transformations and then numerical results were obtained by engaging the blend of Runge–Kutta and shooting techniques. The sway of physical quantities are examined graphically. An excellent agreement within graphical illustration and numerical results is achieved.

Stress and Displacement Analysis of a Shell Intersection

1970 ◽  
Vol 92 (2) ◽  
pp. 303-308 ◽  
Author(s):  
K. C. Pan ◽  
R. E. Beckett
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Internal Pressure ◽  
Numerical Solution ◽  
Numerical Computation ◽  
Cylindrical Shells ◽  
Numerical Results ◽  
Radius Ratio ◽  
Displacement Analysis

The problem of two normally intersecting cylindrical shells subjected to internal pressure is considered. The differential equations used for the shells are solved subject to the boundary conditions imposed along the intersection between the two cylinders. Details of a procedure for obtaining a numerical solution are given. Numerical results for a radius ratio of 1:2 are presented. Problems encountered in the numerical computation are discussed and the results of the analysis are compared with experiment.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1993 ◽  
Vol 115 (3) ◽  
pp. 346-358 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

Derivation of Governing Equations For Self-Acting Foil Bearings

1967 ◽  
Vol 89 (3) ◽  
pp. 334-339 ◽  
Author(s):  
E. J. Barlow
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Bending Stiffness ◽  
The Self ◽  
Governing Equations ◽  
Foil Bearings ◽  
Foil Bearing

Contained is the derivation of the equations for the self-acting foil bearing. These equations include the effects of bending stiffness of the tape and of compressibility of the lubricant. They are nonlinear, and the boundary conditions are divided equally between the two ends of the tape. These complications even make obtaining numerical solutions difficult. Linearized solutions are derived for large wrap angles neglecting the bending stiffness of the tape.

Transient Analysis of a Planar Hybrid Foil-Bearing Model

1974 ◽  
Vol 96 (3) ◽  
pp. 432-435 ◽  
Author(s):  
A. Eshel
Keyword(s):  
Dynamic Behavior ◽  
Transient Analysis ◽  
Initial Conditions ◽  
Foil Bearings ◽  
Foil Bearing

Analysis of the dynamic behavior of planar foil bearings is presented for the case when both self acting and external pressurization effects are present. From it, responses to arbitrary disturbances or initial conditions may be deduced. Graphical examples for the film response to step reduction in tension and to a moving pressurization source are shown.

Spectral Methods

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Simple Model ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Linear Algebra ◽  
Spectral Methods ◽  
Differential Operators ◽  
Higher Dimensions ◽  
Standard Linear ◽  
Sommerfeld Equation ◽  
Spectral Discretization

Thenumerical solution of ordinary differential equations (ODEs)with boundary conditions is studied here. Functions are approximated by polynomials in a Chebychev basis. Sections then cover spectral discretization, sampling, interpolation, differentiation, integration, and the basic ODE. Following Trefethen et al., differential operators are approximated as rectangular matrices. Boundary conditions add additional rows that turn them into square matrices. These can then be diagonalized using standard linear algebra methods. After studying various simple model problems, this method is applied to the Orr–Sommerfeld equation, deriving results originally due to Orszag. The difficulties of pushing spectral methods to higher dimensions are outlined.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

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