Free Rotation of an Elastic Rod With an End Mass

1986 ◽  
Vol 53 (4) ◽  
pp. 864-868 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Angular Momentum ◽  
Large Deformations ◽  
Free Rotation ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Elastic Rod ◽  
Critical Rotation ◽  
Minimum Total Energy ◽  
Equilibrium Configurations ◽  
Flexible Antenna

This paper models a rotating space satellite with a long flexible antenna. Large deformations of the elastic rod are caused by the centrifugal forces. Bifurcation analysis shows the effect of end mass on the critical rotation speeds above which sinuous equilibrium configurations occur. The nonlinear governing equations are then integrated numerically. We find a class of solutions with a looped configuration whose existence requires a certain minimum total energy and minimum angular momentum. Catastrophic changes are possible.

Dynamics of an electrostatically charged elastic rod in fluid

2010 ◽  
Vol 467 (2126) ◽  
pp. 569-590 ◽  
Author(s):  
Sookkyung Lim ◽  
Yongsam Kim ◽  
David Swigon
Keyword(s):  
Immersed Boundary Method ◽  
Stable Equilibrium ◽  
Equations Of Motion ◽  
Initial Perturbation ◽  
Hard Core ◽  
Unstable Equilibrium ◽  
Immersed Boundary ◽  
Governing Equations ◽  
Elastic Rod ◽  
Equilibrium Configurations

We investigate the effects of electrostatic and steric repulsion on the dynamics of a pre-twisted charged elastic rod immersed in a viscous incompressible fluid. Equations of motion of the rod include the fluid–structure interaction, rod elasticity and a combination of two interactions that prevent self-contact, namely the electrostatic interaction and hard-core repulsion. The governing equations are solved using the generalized immersed-boundary method. We find that after perturbation, a pre-twisted minicircle collapses into a compact supercoiled configuration. The collapse proceeds along a complex trajectory that may pass near several unstable equilibrium configurations, before it settles in a locally stable equilibrium. The dwell time near an unstable equilibrium can be up to several microseconds. Both the final configuration and the transition path are sensitive to the initial excess link, ionic strength of the solvent and the initial perturbation.

scholarly journals Equilibrium Configurations of the Noncircular Cross-Section Elastic Rod Model with the Elliptic KB Method

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Yongzhao Wang ◽  
Qichang Zhang ◽  
Wei Wang
Keyword(s):  
Cross Section ◽  
Dynamical Behavior ◽  
Elliptic Functions ◽  
Physical Parameters ◽  
Valuable Insight ◽  
Elastic Rod ◽  
Noncircular Cross Section ◽  
Equilibrium Configurations ◽  
Rational Expressions ◽  
Elastic Rod Model

The mechanical deformation of DNA is very important in many biological processes. In this paper, we consider the reduced Kirchhoff equations of the noncircular cross-section elastic rod characterized by the inequality of the bending rigidities. One family of exact solutions is obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behavior of the system in response to changes in physical parameters that concern asymmetry. The effects of the factor on the DNA conformation are discussed. A qualitative analysis is also conducted to provide valuable insight into the topological configuration of DNA segments.

Thermohydrodynamic Performance of Thrust Bearings With Circular Tilted Pads Under the Presence of Air Gas Bubbles and Centrifugal Forces

1989 ◽  
Vol 111 (3) ◽  
pp. 510-517 ◽  
Author(s):  
L. A. Abdel-Latif ◽  
E. M. Bakr ◽  
M. I. Ghobrial
Keyword(s):  
Gas Bubbles ◽  
Lubricating Oil ◽  
Compressible Medium ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Thrust Bearings ◽  
Characteristic Values ◽  
The Finite Difference Method ◽  
Temperature And Pressure ◽  
Bearing Characteristic

This paper deals with the analysis of thrust bearings with tilted circular pads running under thermohydrodynamic conditions. During operation, a considerable quantity of air/gas bubbles is dispersed inside the lubricating oil and build a compressible medium. The important lubricant properties, namely viscosity and density are altered substantially due to bubble presence as well as temperature rise. The influence of the centrifugal forces become significant as the speed and load become higher. Such type of bearings has been herein investigated taking into account both influencing phenomena. The geometric and loading parameters are varied to show the combined effect on the bearing characteristic values. The governing equations of the THD theory are solved numerically using the finite difference method. The surface tension of bubbles and the change of bubble content with temperature and pressure are included in the governing equations as are the centrifugal forces.

scholarly journals Feasibility of a Quasi-Static Approach in Assessing Side-Wind Hazards for Running Vehicles

2019 ◽  
Vol 9 (16) ◽  
pp. 3377 ◽  
Author(s):  
Se-Jin Kim ◽  
Ho-Kyung Kim
Keyword(s):  
Valuable Insight ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Rolling Moment ◽  
Novel Approach ◽  
Reaction Forces ◽  
Static Approach ◽  
Tire Forces ◽  
Insight Into ◽  
Force Equilibrium

This study is an examination into the feasibility of a quasi-static approach to evaluating the reaction forces that impact tires. This information could lend valuable insight into efforts to limit overturning and side-slip accidents of vehicles exposed to strong side winds. The performance of the quasi-static approach was evaluated by comparing the calculated tire forces with those created using TruckSim, which is a dynamic vehicle analysis software. Governing equations were formulated for two types of vehicles that are susceptible to the force of wind, vans, and trailers, by considering a force equilibrium, a compatibility condition, and several assumptions. The quasi-static approach for trailers is a novel expansion of the conventional approach to a two-axle vehicle. Proposed enhancements to the quasi-static approach reflect the additional rolling moment of a trailer. The curvature and the cant of a curved road were accounted for via centrifugal forces. Both uniform and turbulent wind conditions were considered in questioning the feasibility of this novel approach.

scholarly journals GLOBAL SOLUTIONS OF THE EQUATION OF THE KIRCHHOFF ELASTIC ROD IN SPACE FORMS

2012 ◽  
Vol 88 (1) ◽  
pp. 70-80 ◽  
Author(s):  
SATOSHI KAWAKUBO
Keyword(s):  
Space Form ◽  
Global Solutions ◽  
Infinite Length ◽  
Elastic Rods ◽  
Elastic Rod ◽  
Lagrange Equations ◽  
Initial Value ◽  
Space Forms ◽  
Equilibrium Configurations ◽  
Rod Of Finite Length

AbstractThe Kirchhoff elastic rod is one of the mathematical models of equilibrium configurations of thin elastic rods, and is defined to be a solution of the Euler–Lagrange equations associated to the energy with the effect of bending and twisting. In this paper, we consider Kirchhoff elastic rods in a space form. In particular, we give the existence and uniqueness of global solutions of the initial-value problem for the Euler–Lagrange equations. This implies that an arbitrary Kirchhoff elastic rod of finite length extends to that of infinite length.

Untwist of Rotating Blades

1975 ◽  
Vol 97 (2) ◽  
pp. 180-187 ◽  
Author(s):  
M. Ohtsuka
Keyword(s):  
Cross Section ◽  
Virtual Work ◽  
Axial Flow ◽  
Arbitrary Cross Section ◽  
Principle Of Virtual Work ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Compressor Rotor ◽  
Flow Compressor ◽  
Good Agreement

This paper deals with the deformation and the stress of an axial flow compressor rotor blade under the loading of centrifugal forces. Coupled deformation of extension, bending, torsion and transverse shear of a pretwisted curved bar with arbitrary cross section is considered. Governing equations derived by means of the principle of virtual work are solved numerically by finite difference method. The warping functions used in the analysis were obtained by the use of finite element method. Measurement of the untwist angles and the stresses were carried out for the verification of the numerical analysis and they were found to be in good agreement.

Conservative Formulation of Large Deformation Plasticity

1993 ◽  
Vol 46 (12) ◽  
pp. 519-526 ◽  
Author(s):  
James G. Glimm ◽  
Bradley J. Plohr ◽  
David H. Sharp
Keyword(s):  
High Resolution ◽  
Shear Band ◽  
Large Deformation ◽  
Large Deformations ◽  
Shear Bands ◽  
Shock Capturing ◽  
Jump Discontinuity ◽  
Governing Equations ◽  
Conservative Form ◽  
Deformation Plasticity

We explain several ideas which may, either singly or in combination, help achieve high resolution in simulations of large-deformation plasticity. Because of the large deformations, we work in the Eulerian picture. The governing equations are written in a fully conservative form, which are correct for discontinuous as well as continuous solutions. Models of shear bands are discussed. These models describe the internal dynamics of a developed shear band in terms of time-asymptotic states; in other words, the smooth internal structure is replaced by a jump discontinuity, and the shear band evolution is determined by jump relations. This analysis is useful for high resolution numerical methods, including both shock capturing and shock tracking schemes, as well as for the understanding and validation of computations, independently of the underlying method. Preliminary computations, which illustrate the feasibility of these ideas, are presented.

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