Asymptotic analysis and numerical solutions for the rigid body containing a viscous liquid in cavity in the presence of gyrostatic moment

2021 ◽  
Author(s):  
W. S. Amer ◽  
A. M. Farag ◽  
I. M. Abady
Keyword(s):  
Asymptotic Analysis ◽  
Rigid Body ◽  
Viscous Liquid ◽  
Numerical Solutions

scholarly journals Inertial motions of a rigid body with a cavity filled with a viscous liquid

2013 ◽  
Vol 341 (11-12) ◽  
pp. 760-765 ◽  
Author(s):  
Giovanni P. Galdi ◽  
Giusy Mazzone ◽  
Paolo Zunino
Keyword(s):  
Rigid Body ◽  
Viscous Liquid

scholarly journals The Dynamical Behavior of a Rigid Body Relative Equilibrium Position

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
T. S. Amer
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Relative Equilibrium ◽  
Dynamical Behavior ◽  
Vertical Plane ◽  
The Body ◽  
Physical Parameters ◽  
Pendulum Model

In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures.

Numerical Solutions of Polynomial Equations for the Eight-Position Synthesis of the Cylindrical-Spherical Dyad

2012 ◽  
Author(s):  
Chintien Huang ◽  
Chenning Hung ◽  
Kuenming Tien
Keyword(s):  
Rigid Body ◽  
Numerical Solutions ◽  
Continuation Method ◽  
Quadratic Equation ◽  
Geometric Constraints ◽  
Numerical Continuation ◽  
Polynomial Equations ◽  
Quartic Polynomial ◽  
Solutions Of Equations ◽  
Position Synthesis

This paper investigates the numerical solutions of equations for the eight-position rigid-body guidance of the cylindrical-spherical (C-S) dyad. We seek to determine the number of finite solutions by using the numerical continuation method. We derive the design equations using the geometric constraints of the C-S dyad and obtain seven quartic polynomial equations and one quadratic equation. We then solve the system of equations by using the software package Bertini. After examining various specifications, including those with random complex numbers, we conclude that there are 804 finite solutions of the C-S dyad for guiding a body through eight prescribed positions. When designing spatial dyads for rigid-body guidance, the C-S dyad is one of the four dyads that result in systems of equal numbers of equations and unknowns if the maximum number of allowable positions is specified. The numbers of finite solutions in the syntheses of the other three dyads have been obtained previously, and this paper provides the computational kinematic result of the last unsolved problem, the eight-position synthesis of the C-S dyad.

Mitigation of Rocking and Sliding Motion of a Free-Standing Structure Subjected to Base Excitation Using Coaxial Circular Cylinders Containing Highly Viscous Liquid in Annular Spaces

2019 ◽  
Author(s):  
Atsuhiko Shintani ◽  
Tomohiro Ito ◽  
Chihiro Nakagawa
Keyword(s):  
Rigid Body ◽  
Viscous Liquid ◽  
Analytical Model ◽  
Circular Cylinders ◽  
Base Excitation ◽  
Free Standing ◽  
Seismic Input ◽  
Sliding Motion ◽  
Standing Structure ◽  
Rocking Motion

Abstract In this study, the effectiveness of coaxial circular cylinders containing a highly viscous liquid in annular spaces for reduction of rocking motion of a free-standing structure is investigated both analytically and experimentally. First, an analytical model of coupled rocking and sliding motions of a free-standing structure, including the coaxial circular cylinders, subjected to seismic input was derived. The free-standing structure was modeled as a free-standing rigid body. The cylinders were attached to the bottom of the rigid body as a damping device. We then experimentally derived the friction coefficients, inertia moments, and a damping coefficient in the rotating direction. Furthermore, using these parameters, the effectiveness of this system in suppressing the rocking motion is investigated analytically. The proposed method was determined to be very effective in suppressing the rocking motion of a rigid body subjected to a seismic input by the experiment.

scholarly journals Analysis of electro-permeation of hydrogen in metallic alloys

2017 ◽  
Vol 375 (2098) ◽  
pp. 20160409 ◽  
Author(s):  
A. Raina ◽  
V. S. Deshpande ◽  
N. A. Fleck
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Solutions ◽  
Local Equilibrium ◽  
Reaction Diffusion ◽  
Metallic Alloys ◽  
Diffusion Type ◽  
Thermal Desorption Spectrometry ◽  
Modelling Framework ◽  
Numerical Predictions ◽  
Study Support

A reaction–diffusion type modelling framework is presented to analyse both electro-permeation (EP) and thermal desorption spectrometry (TDS) measurements of hydrogen in metallic alloys. It is assumed that the kinetics of hydrogen motion is governed by diffusion through the lattice, along with trapping/detrapping at specific sites such as dislocations, grain boundaries, etc. It is shown that the trapping and detrapping rates are typically much faster than the diffusion rate, and consequently a simplification of the governing equations suffices such that local equilibrium exists between lattice and trapped hydrogen. Using this local equilibrium assumption, we then present an asymptotic analysis of the governing kinetic equation for the EP test. This asymptotic analysis reveals that four regimes of behaviour exist, ranging from negligible trapping to the complete filling of deep traps. The analysis suggests that EP tests should be so-arranged that three regimes of behaviour are spanned, in order to extract the relevant material properties associated with hydrogen transport. The numerical solutions presented in this study support the asymptotic analysis. The hydrogen kinetics framework is also deployed to analyse both EP and TDS tests on the same martensitic steel. The EP measurements all lie in regime I and are thus insufficient to uniquely determine both the trap density and binding energy. Reasonable agreement is obtained between measurements and numerical predictions of TDS tests using parameters estimated from the EP tests. Further improvements in measurements are required to confirm the fidelity of this modelling approach. This article is part of the themed issue ‘The challenges of hydrogen and metals’.

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