Thermal entry region analysis through the finite integral transform technique in laminar flow of Bingham fluids within concentric annular ducts

2002 ◽  
Vol 45 (4) ◽  
pp. 923-929 ◽  
Author(s):  
U.C.S. Nascimento ◽  
E.N. Macêdo ◽  
J.N.N. Quaresma
Keyword(s):  
Laminar Flow ◽  
Integral Transform ◽  
Bingham Fluids ◽  
Region Analysis ◽  
Finite Integral ◽  
Integral Transform Technique

Analytical Solution of Forced Vibration of a Column Subjected to Conservative and Nonconservative Forces

2001 ◽  
Author(s):  
Zhixiang Xu ◽  
Kunisato Seto ◽  
Hideyuki Tamura
Keyword(s):  
Analytical Solution ◽  
Boundary Value Problem ◽  
Integral Transform ◽  
Boundary Value ◽  
Suspension Bridge ◽  
Follower Force ◽  
Analysis Process ◽  
Finite Integral ◽  
Excitation Force ◽  
Integral Transform Technique

Abstract This paper presents analytical results of forced transverse vibration of a column with a mass attached at free-end subjected to a tangential follower force and a transverse distributed excitation force, that is a simplified model of some structures in civil and mechanical engineering, e.g., a column of a suspension bridge, a launched rocket in the atmosphere. Because the tangential follower force is nonconservative, it is very difficult to get the analytical solution of the problem by usually-used analysis methods with which the adjoint boundary value problem can not be directly obtained. However, by applying the finite integral transform technique, we directly obtained the adjoint boundary value problem in the analysis process, and successfully obtained the analytical solution of the column’s vibration excited by the transverse distributed force.

Analysis of the Natural Vibration Properties of a Timoshenko Beam Supported by Springs (by Finite Integral Transform Method)

1999 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura ◽  
Kunisato Seto
Keyword(s):  
Timoshenko Beam ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Integral Transform ◽  
Frequency Equation ◽  
Transform Method ◽  
Vibration Problem ◽  
Vibration Properties ◽  
Finite Integral ◽  
Integral Transform Technique

Abstract This paper presents analytical results of transverse vibration of a Timoshenko beam supported by spring-spring which stiffness is variable, that is a simplified model of magnetically levitated vehicle body’s vibration problem and magnetic bearings support shaft’s vibration problem. By applying the finite integral transform technique, the analytical solution of this dynamic model is successfully obtained. Especially, by investigating the frequency equation, the effect of the stiffness of two supporting-springs to the natural frequencies is clarified. From the results, it is cleared that the natural frequencies of the beam system can be effectively controlled by changing the supporting-spring’s stiffness.

Hybrid Analytical-Numerical Analysis of SAE 4150 Alloy Steel Rods Cooling

2014 ◽  
Vol 1082 ◽  
pp. 187-190 ◽  
Author(s):  
Marcelo Ferreira Pelegrini ◽  
Thiago Antonini Alves ◽  
Felipe Baptista Nishida ◽  
Ricardo A. Verdú Ramos ◽  
Cassio R. Macedo Maia
Keyword(s):  
Diffusion Equation ◽  
Alloy Steel ◽  
Integral Transform ◽  
Numerical Study ◽  
Physical Parameters ◽  
Analytical Treatment ◽  
Aspect Ratios ◽  
Rectangular Cylinders ◽  
Thermo Physical Properties ◽  
Integral Transform Technique

In this work, a hybrid analytical-numerical study was performed in cooling of rectangular rods made from SAE 4150 alloy steel (0.50% carbon, 0.85% chrome, 0.23% molybdenum, and 0.30% silicon). The analysis can be represented by the solution of transient diffusive problems in rectangular cylinders with variable thermo-physical properties in its domain under the boundary conditions of first kind (Dirichlet condition) and uniform initial condition. The diffusion equation was linearized through the Kirchhoff Transformation on the temperature potential to make the analytical treatment easier. The Generalized Integral Transform Technique (GITT) was applied on the diffusion equation in the domain in order to determine the temperature distribution. The physical parameters of interest were determined for several aspect ratios and compared with the results obtained through numerical simulations using the commercial software ANSYS/FluentTM15.

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