Asymptotic Theory of Unsteady Three-Dimensional Waves in a Channel of Arbitrary Cross Section

1969 ◽  
Vol 17 (2) ◽  
pp. 260-271 ◽  
Author(s):  
M. C. Shen
Keyword(s):  
Cross Section ◽  
Asymptotic Theory ◽  
Three Dimensional ◽  
Arbitrary Cross Section

Vibration of Stress-Free Hollow Cylinders of Arbitrary Cross Section

1995 ◽  
Vol 62 (3) ◽  
pp. 718-724 ◽  
Author(s):  
K. M. Liew ◽  
K. C. Hung ◽  
M. K. Lim
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Width Ratio ◽  
Cross Sectional ◽  
Hollow Cylinders ◽  
Displacement Based ◽  
Bending Modes

A three-dimensional elasticity solution to the vibrations of stress-free hollow cylinders of arbitrary cross section is presented. The natural frequencies and deformed mode shapes of these cylinders are obtained via a three-dimensional displacement-based energy formulation. The technique is applied specifically to the parametric investigation of hollow cylinders of different cross sections and sizes. It is found that the cross-sectional property of the cylinder has significant effects on the normal mode responses, particularly, on the transverse bending modes. By varying the length-to-width ratio of these elastic cylinders, interesting results demonstrating the dependence of frequencies on the length of the cylinder have been concluded.

Beam Theory and Its Suitability for the Analysis of Pipes

1991 ◽  
Vol 113 (2) ◽  
pp. 291-296
Author(s):  
H. Fan ◽  
G. E. O. Widera ◽  
P. Afshari
Keyword(s):  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
Cross Section ◽  
Three Dimensional ◽  
Beam Theory ◽  
Arbitrary Cross Section ◽  
Elasticity Equations ◽  
Expansion Technique ◽  
Three Dimensional Elasticity ◽  
Benchmark Solutions

The use of the asymptotic expansion technique when applied to the three-dimensional elasticity equations is outlined and used to demonstrate the development of an asymptotic beam theory and associated boundary conditions. The formulation thus obtained holds for arbitrary cross section shapes and is applied here to pipes. It can be used to provide benchmark solutions to test the suitability of engineering beam and shell theories.

Stresses in a Helical Spring of Arbitrary Cross Section With Consideration of End Effects

1987 ◽  
Vol 109 (3) ◽  
pp. 289-301 ◽  
Author(s):  
K. Nagaya
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Beam Theory ◽  
Theory Of Elasticity ◽  
Arbitrary Cross Section ◽  
Coil Spring ◽  
End Effects ◽  
Free Boundary Conditions ◽  
Resultant Forces ◽  
Stress Free Boundary

This paper presents expressions for stresses in the spring due to compression or tension in the direction of the axis of the cylindrical coil. In deriving stresses in the spring, it is necessary to first obtain resultant forces and resultant moments which occur in the coil spring. Then the analysis first derives exact results based on three-dimensional curved beam theory in which all displacements and all forces in three orthogonal directions of the coil spring are included with consideration of the constraints of the ends of the spring. Since the boundary shape of the spring is irregular, it is also difficult to satisfy stress-free boundary conditions along the surface of the coil, so that this paper applies the Fourier expansion collocation method and obtains stresses in the coil spring based on the theory of elasticity.

A Simple Method for the Design of Supersonic Nozzles of Arbitrary Cross Section Shape

2020 ◽  
Author(s):  
N. Boughazi ◽  
A. Haddad
Keyword(s):  
Cross Section ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Simple Method ◽  
Supersonic Nozzles ◽  
De Laval Nozzle

Abstract A simple approach for the design of supersonic nozzles of complex 3D shapes is presented. The Method of characteristics is primarily applied to compute the axisymmetric flow field of the supersonic section of the de-Laval nozzle. Two-dimensional simulations are performed for the axisymmetric flow fields. The 3D configuration is then generated from the desired exit axisymmetric cross-sectional shape chosen through tracing its geometrical parameters back.to the throat. Elliptical, corrugated and two-dimensional wedge nozzles were designed using this approach. Preliminary results show a smooth geometrical transition from the throat to the exit cross section. Further three-dimensional analyses of the obtained geometries along with cold flow testing constitute the next steps to be performed.

Flow in Slowly Varying Microchannels of Rectangular Cross-Section

2009 ◽  
Author(s):  
Mohsen Akbari ◽  
David Sinton ◽  
Majid Bahrami
Keyword(s):  
Cross Section ◽  
Numerical Study ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Numerical Data ◽  
Arbitrary Cross Section ◽  
Fully Developed Flow ◽  
Deviation Factor ◽  
Channel Aspect Ratio ◽  
Compact Models

Laminar fully developed flow in streamwise-periodic microchannels of rectangular cross-section has been studied in this work. Based on the lubrication approximation, an analytical approach is proposed for the frictional flow resistance. Using the analytical model developed for straight channels of arbitrary cross-section, compact models are developed for linear and sinusoidal wall shapes. The models are then examined with two asymptotic two-dimensional flows of: (a) very narrow and (b) very tall channels and compared with the available experimental and numerical data in the literature. An independent numerical study is also performed to evaluate the proposed models for the three-dimensional flow case. Effects of the channel aspect ratio and deviation factor on the pressure drop are also investigated. Results for the three-simensional flow show that the proposed compact models capture the trend of the numerical data with good accuracy.

Sign in / Sign up

Export Citation Format

Share Document