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

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.

Thermal Resistance Approach: An Engineering Tool for Improvement of Conductive Constructal Configurations

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
M. Eslami ◽  
K. Jafarpur
Keyword(s):  
Numerical Methods ◽  
Thermal Resistance ◽  
Cross Section ◽  
Mathematical Formulation ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Effective Parameters ◽  
Total Thermal Resistance ◽  
Profound Knowledge ◽  
Resistance Approach

In the last decade, various conductive networks for cooling heat generating bodies have been proposed, analyzed, and optimized. Nevertheless, many of these studies have not been based on an analytical or mathematical formulation of the effective parameters. In this trend, a new geometry is assumed and analyzed (by analytical or numerical methods) hoping to decrease the total thermal resistance of the system. Therefore, the objective of the present paper is to illustrate how to analyze a conductive cooling network and improve it using the analytical procedures based on the general formulation of thermal resistance. As an example, the conventional rectangular elemental volumes with I shaped conductive link is modified to V shaped and pencil shaped designs and optimized analytically. Moreover, general expressions for optimum local thickness and thermal resistance of the links with variable cross section in an arbitrary network are provided. It is shown that improvements up to 50% can be achieved easily by simple geometrical changes if the designer is equipped with a profound knowledge of the important governing parameters.

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.

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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