The Unsteady Potential Flow in an Axially Variable Annulus and Its Effect on the Dynamics of the Oscillating Rigid Center-Body

1985 ◽  
Vol 107 (3) ◽  
pp. 421-427 ◽  
Author(s):  
Dan Mateescu ◽  
Michael P. Paidoussis
Keyword(s):  
Potential Flow ◽  
Fluid Dynamic ◽  
Variable Cross Section ◽  
Analytical Investigation ◽  
Accurate Solution ◽  
Variable Cross ◽  
Approximation Solution ◽  
Dynamic Forces ◽  
The Stability ◽  
Center Body

This paper presents an analytical investigation of the unsteady potential flow in a narrow annular passage formed by a motionless rigid duct and an oscillating rigid center-body, both of axially variable cross section, in order to determine the fluid-dynamic forces exerted on the center-body. Based on this theory, a first-approximation solution as well as a more accurate solution are derived for the unsteady incompressible fluid flow. The stability of the center-body is investigated, in terms of the aerodynamic (or hydrodynamic) coefficients of damping, stiffness and inertia (virtual mass), as determined by this theory. The influence of various system parameters on stability is discussed.

A Different Method to Evaluate the Intact Stability of Floating Structures

1983 ◽  
Vol 20 (01) ◽  
pp. 21-25
Author(s):  
Abobakr M Radwan
Keyword(s):  
Mathematical Formulation ◽  
Variable Cross Section ◽  
Regulatory Body ◽  
Variable Cross ◽  
Buoyant Force ◽  
Floating Structures ◽  
Intact Stability ◽  
Correct Location ◽  
The Stability ◽  
Heeling Moment

A mathematical formulation of a computer-based method to evaluate the intact stability of floating structures is presented. The technique depends on describing the surface of the structure in terms of many small finite elements, which allows the analysis of complicated hull geometry, determining the hydrostatic pressure on each element for a known heel angle, and integrating the pressure forces to find the magnitude, direction, and line of action of the buoyant force. This will result in the correct location of the metacenter for small, as well as large, angles of heel. For structures of variable cross section, the position of the heeled vessel in equilibrium is defined such that the weight is balanced by the buoyant force, and only a pure righting moment associated with the heeling angle is evaluated. Formulation for the wind heeling moment is also presented. Assessment of the stability of the vessel is made from the righting and heeling moment curves in light of regulatory body rules.

scholarly journals On the Stability of Rod with Variable Cross-section

2015 ◽  
Vol 111 ◽  
pp. 42-48
Author(s):  
Vladimir I. Andreev ◽  
Nikita Y. Tsybin
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
The Stability

Nonlinear Stability Analysis of a Two-Dimensional Model of an Elastic Tube Conveying a Compressible Flow

1979 ◽  
Vol 46 (1) ◽  
pp. 31-36 ◽  
Author(s):  
Y. Matsuzaki ◽  
Y.-C. Fung
Keyword(s):  
Fluid Dynamic ◽  
Elastic Tube ◽  
Two Dimensional ◽  
Nonlinear Stability Analysis ◽  
Internal Wall ◽  
Equilibrium Configurations ◽  
Dynamic Forces ◽  
Unsteady Fluid ◽  
The Stability ◽  
Small Disturbances

This paper examines the dynamic behavior of a two-dimensional channel whose upper and lower walls deform symmetrically with respect to the center line of the channel. Unsteady fluid dynamic forces acting on the internal wall are analytically evaluated on the basis of a linearized compressible potential flow theory. The effects of distributed springs outside the channel and an internal pressure on the stability characteristics are studied by considering small disturbances about flat and buckled equilibrium configurations of the wall. The analytic methods indicate that no flutter of the flat or buckled wall is predicted when the Mach number is small and the viscous damping coefficient is positive. Numerical results by the Runge-Kutta-Gill method suggest that nonlinear effect of flow should be taken into account to fully examine the dynamic characteristics of the channel conveying a flow.

scholarly journals Limits of Riemann solutions for isentropic MHD in a variable cross-section duct as magnetic field vanishes

2021 ◽  
Author(s):  
Wancheng Sheng ◽  
Tao Xiao
Keyword(s):  
Magnetic Field ◽  
Riemann Problem ◽  
Cross Section ◽  
Variable Cross Section ◽  
Field Method ◽  
Variable Cross ◽  
Riemann Solutions ◽  
Stable Solutions ◽  
The Stability ◽  
Limit Solutions

The stability for magnetic field to the solution of the Riemann problem for the polytropic fluid in a variable cross-section duct is discussed. By the vanishing magnetic field method, the stable solutions are determined by comparing the limit solutions with the solutions of the Riemann problem for the polytropic fluid in a duct obtained by the entropy rate admissibility criterion.

scholarly journals Behavior of Steel Welded Tapered Beam-column

2017 ◽  
Vol 11 (1) ◽  
pp. 345-357 ◽  
Author(s):  
A.I. Dogariu ◽  
A. Crișan ◽  
M. Cristuțiu ◽  
D.L. Nunes ◽  
A. Juca
Keyword(s):  
Bending Moment ◽  
Experimental Tests ◽  
Variable Cross Section ◽  
Analytical Investigation ◽  
Variable Cross ◽  
Structural Elements ◽  
Beam Columns ◽  
Tapered Beam ◽  
Load Combination ◽  
Tapered Members

Steel structural elements with variable cross-section, made of welded plates, are largely used in the construction industry for both beams and columns in accordance with the stress and stiffness demand in the structure. These types of elements are mainly used for the design of single storey frames with pitched roof rafters and pinned column base. Rafters and columns can be designed as tapered members made of steel welded plates, respecting the bending moment diagrams for gravitational load combination. This paper deals with experimental tests performed on tapered beam-columns elements, subjected to both bending moment and compressive axial force together with analytical investigation.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

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