scholarly journals Equilibrium shapes of nonaxisymmetric liquid bridges of arbitrary volume in gravitational fields and their potential energy

1995 ◽  
Vol 7 (6) ◽  
pp. 1204-1213 ◽  
Author(s):  
Ana Laverón‐Simavilla ◽  
José M. Perales
Keyword(s):  
Potential Energy ◽  
Liquid Bridges ◽  
Gravitational Fields ◽  
Equilibrium Shapes ◽  
Arbitrary Volume

scholarly journals Vortex-Induced Vibration: the slower deceleration of the west bank leads to the shortening of the Humen Bridge in Guangdong, China

2020 ◽  
Author(s):  
Haili Ran ◽  
Xiaoyong Lu ◽  
Ruohan Zheng ◽  
Cui Yang ◽  
Qiuyun Liu
Keyword(s):  
Potential Energy ◽  
Civil Engineering ◽  
West Bank ◽  
Large Mass ◽  
Small Mass ◽  
The West ◽  
Vortex Induced Vibration ◽  
Gravitational Fields ◽  
The Earth ◽  
Engineering Projects

The Earth self-rotates in the solar and lunar gravitational fields. According to Newton’s Law of Inertia, large mass accelerates and decelerates more slowly than smaller masses, whereas small mass accelerates and decelerates more quickly than larger mass, which gives rise to stress when potential energy is present, damaging civil engineering projects. Humen Bridge of Guangdong, China and two century-old dams in Michigan which were affected recently can be explained by this theory.

Review on the Dynamics of Isothermal Liquid Bridges

2019 ◽  
Vol 72 (1) ◽  
Author(s):  
José M. Montanero ◽  
Alberto Ponce-Torres
Keyword(s):  
Nonlinear Behavior ◽  
Forced Oscillations ◽  
Liquid Bridges ◽  
Contact Lines ◽  
Surfactant Monolayers ◽  
Weakly Nonlinear ◽  
Nonlinear Motion ◽  
Bridge Problem ◽  
Equilibrium Shapes ◽  
Streaming Flows

Abstract In this review, we describe both theoretical and experimental results on the dynamics of liquid bridges under isothermal conditions with fixed triple contact lines. These two major restrictions allow us to focus on a well-defined body of literature, which has not as yet been reviewed in a comprehensive way. Attention is mainly paid to liquid bridges suspended in air, although studies about the liquid–liquid configuration are also taken into account. We travel the path from equilibrium to nonlinear dynamics of both Newtonian liquid bridges and those made of complex fluids. Specifically, we consider equilibrium shapes and their stability, linear dynamics in free and forced oscillations under varied conditions, weakly nonlinear behavior leading to streaming flows, fully nonlinear motion arising during stretching and breakup of liquid bridges, and problems related to rheological effects and the presence of surfactant monolayers. Although attention is mainly paid to fundamental aspects of these problems, some applications derived from the results are also mentioned. In this way, we intend to connect the two approaches to the liquid bridge problem, something that both theoreticians and experimentalists may find interesting.

Stability of Magnetically Levitated Liquid Bridges of Arbitrary Volume Subjected to Axial and Lateral Gravity

1999 ◽  
Vol 213 (2) ◽  
pp. 592-595 ◽  
Author(s):  
Milind P. Mahajan ◽  
Shiyong Zhang ◽  
Mesfin Tsige ◽  
P.L. Taylor ◽  
Charles Rosenblatt
Keyword(s):  
Liquid Bridges ◽  
Magnetically Levitated ◽  
Arbitrary Volume

Finite Element Method for Predicting Equilibrium Shapes of Solder Joints

1993 ◽  
Vol 115 (2) ◽  
pp. 141-146 ◽  
Author(s):  
N. J. Nigro ◽  
S. M. Heinrich ◽  
A. F. Elkouh ◽  
X. Zou ◽  
R. Fournelle ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Potential Energy ◽  
Solder Joints ◽  
Thermal Analyses ◽  
Joint Surface ◽  
Parametric Form ◽  
Nodal Coordinates ◽  
Equilibrium Shapes ◽  
Element Method

This paper discusses the development and application of a finite element method for determining the equilibrium shapes of solder joints which are formed during a surface mount reflow process. The potential energy governing the joint formation problem is developed in the form of integrals over the joint surface, which is discretized with the use of finite elements. The spatial variables which define the shape of the surface are expressed in a parametric form involving products of interpolation (blending) functions and element nodal coordinates. The nodal coordinates are determined by employing the minimum potential energy theorem. The method described in this paper is very general and can be employed for those problems involving the formation of three dimensional joints with complex shapes. It is well suited for problems in which the boundary region is not known a priori (e.g., “infinite tinning” problems). Moreover, it enables the user to determine the shape of the joint in parametric form which facilitates meshing for subsequent finite element stress and thermal analyses.

scholarly journals GEODYNAMICS

GEODYNAMICS ◽  
2021 ◽  
Vol 2(31)2021 (2(31)) ◽  
pp. 5-15
Author(s):  
Alexander. N. Marchenko ◽  
◽  
Serhii Perii ◽  
Ivan Pokotylo ◽  
Zoriana Tartachynska ◽  
...  
Keyword(s):  
Solar System ◽  
Potential Energy ◽  
Density Distribution ◽  
Gravitational Potential ◽  
Gravitational Potential Energy ◽  
Normal Density ◽  
Gravitational Fields ◽  
Outer Planets ◽  
Gaussian Density ◽  
Gravitational Problem

The basic goal of this study (as the first step) is to collect the appropriate set of the fundamental astronomic-geodetics parameters for their further use to obtain the components of the density distributions for the terrestrial and outer planets of the Solar system (in the time interval of more than 10 years). The initial data were adopted from several steps of the general way of the exploration of the Solar system by iterations through different spacecraft. The mechanical and geometrical parameters of the planets allow finding the solution of the inverse gravitational problem (as the second stage) in the case of the continued Gaussian density distribution for the Moon, terrestrial planets (Mercury, Venus, Earth, Mars) and outer planets (Jupiter, Saturn, Uranus, Neptune). This law of Gaussian density distribution or normal density was chosen as a partial solution of the Adams-Williamson equation and the best approximation of the piecewise radial profile of the Earth, including the PREM model based on independent seismic velocities. Such conclusion already obtained for the Earth’s was used as hypothetic in view of the approximation problem for other planets of the Solar system where we believing to get the density from the inverse gravitational problem in the case of the Gaussian density distribution for other planets because seismic information, in that case, is almost absent. Therefore, if we can find a stable solution for the inverse gravitational problem and corresponding continue Gaussian density distribution approximated with good quality of planet’s density distribution we come in this way to a stable determination of the gravitational potential energy of the terrestrial and giant planets. Moreover to the planet’s normal low, the gravitational potential energy, Dirichlet’s integral, and other planets’ parameters were derived. It should be noted that this study is considered time-independent to avoid possible time changes in the gravitational fields of the planets.

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