scholarly journals Planar vibration of a thin elastic rod with circular cross section in viscous medium

2005 ◽  
Vol 54 (11) ◽  
pp. 4989
Author(s):  
Liu Yan-Zhu
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Viscous Medium ◽  
Elastic Rod ◽  
Planar Vibration ◽  
Thin Elastic Rod

Axially Symmetric Waves in Elastic Rods

1960 ◽  
Vol 27 (1) ◽  
pp. 145-151 ◽  
Author(s):  
R. D. Mindlin ◽  
H. D. McNiven
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Rods ◽  
Axially Symmetric ◽  
Elastic Rod ◽  
One Dimensional ◽  
Axial Shear ◽  
Wave Numbers ◽  
Complex Wave

A system of approximate, one-dimensional equations is derived for axially symmetric motions of an elastic rod of circular cross section. The equations take into account the coupling between longitudinal, axial shear, and radial modes. The spectrum of frequencies for real, imaginary, and complex wave numbers in an infinite rod is explored in detail and compared with the analogous solution of the three-dimensional equations.

scholarly journals Branching and Stability of Elasic Rod Equilibrium Forms

2021 ◽  
Author(s):  
Dmitrii Skubov ◽  
Dmitry Yu. Kopnin
Keyword(s):  
Differential Equation ◽  
Boundary Problem ◽  
Cross Section ◽  
Compressive Load ◽  
Elliptic Functions ◽  
Vertical Position ◽  
Loss Of Stability ◽  
Elastic Rod ◽  
Turn Angle ◽  
Thin Elastic Rod

Abstract In our article from the positions of branching theory the classical Euler task about stability of thin elastic rod under action of vertical compressive load is considered. With using of turn-tensor and accompanying vector the deformation of rod is described. In result the conditions of equilibrium in a case of linear determining equation are reduced to boundary problem relatively turn angle of cross section, described by the differential equation of pendulum. With help elliptic functions the diagrams of branching are constructed and are received the exact formulas of rod deformation at the loss of stability of vertical position. Analogy the task of stability of rod at turned force on end of rod is considered. Also, the oscillating loss of rod stability at tracking load is studied.

Effect of contributions from bending in evaluation of axial strain in rods with circular cross-section

1983 ◽  
Vol 18 (1) ◽  
pp. 77-79 ◽  
Author(s):  
L Lagerkvist ◽  
K-G Sundin ◽  
B Lundberg
Keyword(s):  
Cross Section ◽  
Axial Strain ◽  
Circular Cross Section ◽  
Strain Gauges ◽  
Elastic Rod ◽  
Simple Method ◽  
Strain Measurements ◽  
Absolute Value ◽  
Bending Strain ◽  
Good Agreement

Contributions from bending to the evaluated axial strain in an elastic rod are commonly suppressed by forming half the sum of measured surface strains at diametrically opposite positions. A simple method is presented which gives a useful estimation of the bending suppression (the ratio of the bending strain to the absolute value of the evaluated axial strain when a rod is subject to bending only) from (i) optically measured mis-positioning, and (ii) estimated differences between the gauge constants for the two strain gauges. Good agreement is obtained with results obtained from strain measurements on a rod loaded in bending.

On the deflected configuration of a slender elastic rod subject to parallel terminal forces and moments

1995 ◽  
Vol 449 (1936) ◽  
pp. 337-349 ◽  
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Cartesian Coordinate System ◽  
Elastic Rod ◽  
Equilibrium Equations ◽  
Elastic Deformations ◽  
Nonlinear Equilibrium ◽  
Cartesian Coordinate ◽  
Nonlinear Elastic

This paper investigates the three-dimensional configurations of a slender elastic rod of uniform circular cross-section subject to parallel terminal forces and moments. The nonlinear, equilibrium equations for the rod are established for a Cartesian coordinate system and solved analytically without linearization. Consequently, the results are applicable for large nonlinear elastic deformations.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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