Forced Motions of Elastic Rods

1954 ◽  
Vol 21 (3) ◽  
pp. 221-224
Author(s):  
G. Herrmann
Keyword(s):  
Equation Of Motion ◽  
Elastic Rod ◽  
Dimensional Theory ◽  
Compressional Waves ◽  
One Dimensional ◽  
Forced Motion ◽  
Lagrange’S Equation ◽  
Rod Theory ◽  
Dependent Variables ◽  
The One

Abstract In a recent paper by Mindlin and Herrmann, a one-dimensional theory of compressional waves in an elastic rod was described. This theory takes into account both radial inertia and radial shear stress and, accordingly, contains two dependent variables instead of the one axial displacement of classical rod theory. The solution of the equations for the case of forced motions thus involves complications not usually encountered. The difficulties may be surmounted in several ways, one of which is presented in this paper. The method described makes use of Lagrange’s equation of motion and reduces the most general problem of forced motion to a free vibration problem and a quadrature.

Alternative derivation of the Claerbout equations

Geophysics ◽  
1978 ◽  
Vol 43 (7) ◽  
pp. 1543-1545
Author(s):  
M. R. Foster ◽  
C. E. Laird
Keyword(s):  
Higher Dimensions ◽  
Equation Of Motion ◽  
One Dimension ◽  
Particle Displacement ◽  
Dimensional Theory ◽  
Alternative Derivation ◽  
One Dimensional ◽  
Reflectivity Function ◽  
The One ◽  
Compressional Velocity

This paper is basically an extension to higher dimensions of the one‐dimensional theory developed by Foster (1975). We begin by briefly reviewing these ideas. In one dimension, the equation of motion for the particle displacement u is given by [Formula: see text]where [Formula: see text] is the vertical traveltime, and [Formula: see text] is the reflectivity function. ρ and c are, respectively, the density and compressional velocity.

scholarly journals LOCAL FRACTIONAL SUPERSYMMETRY FOR ALTERNATIVE STATISTICS

1996 ◽  
Vol 11 (11) ◽  
pp. 899-913 ◽  
Author(s):  
N. FLEURY ◽  
M. RAUSCH DE TRAUBENBERG
Keyword(s):  
Group Theory ◽  
Braid Group ◽  
Equation Of Motion ◽  
Coset Space ◽  
One Dimensional ◽  
The One

A group theory justification of one-dimensional fractional supersymmetry is proposed using an analog of a coset space, just like the one introduced in 1-D supersymmetry. This theory is then gauged to obtain a local fractional supersymmetry, i.e. a fractional supergravity which is then quantized à la Dirac to obtain an equation of motion for a particle which is in a representation of the braid group and should describe alternative statistics. A formulation invariant under general reparametrization is given by means of a curved fractional superline.

scholarly journals CFD tool application in predicting the behavior of a centrifugal fan designed by one-dimensional theory

2021 ◽  
Vol 10 (12) ◽  
pp. e412101219653
Author(s):  
Henrique Marcio Pereira Rosa ◽  
Gabriela Pereira Toledo
Keyword(s):  
Velocity Distribution ◽  
Cfd Simulation ◽  
Centrifugal Fan ◽  
Dimensional Theory ◽  
Recovery Coefficient ◽  
Characteristic Curves ◽  
One Dimensional ◽  
Ansys Cfx ◽  
Computational Fluid Dynamics Cfd ◽  
The One

Computational fluid dynamics (CFD) is the most current technology in the fluid flow study. Experimental methods for predicting the turbomachinery performance involve greater time consumption and financial resources compared to the CFD approach. The purpose of this article is to present the analysis of CFD simulation results in a centrifugal fan. The impeller was calculated using the one-dimensional theory and the volute the principle of constant angular momentum. The ANSYS-CFX software was used for the simulation. The turbulence model adopted was the SST. The simulation provided the characteristic curves, the pressure and velocity distribution, and the static and total pressure values at impeller and volute exit. An analysis of the behavior of the pressure plots, and the loss and recovery of pressure in the volute was performed. The results indicated the characteristic curves, the pressure and velocity distribution were consistent with the turbomachinery theory. The pressure values showed the static pressure at volute exit was smaller than impeller exit for some flow rate. It caused the pressure recovery coefficient negative.  This work indicated to be possible design a centrifugal fan applying the one-dimensional theory and optimize it with the CFD tool.

Taylor Cylinder Testing of High Strength Steels for Hard Target Warhead Applications

2009 ◽  
Author(s):  
Rachel Russo ◽  
Nicholas Dutton ◽  
Bart Baker ◽  
Karen Torres ◽  
Stanley E. Jones ◽  
...  
Keyword(s):  
Impact Test ◽  
True Strain ◽  
High Strength Steels ◽  
High Strength ◽  
True Stress ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Cylinder Test ◽  
Taylor Impact ◽  
The One

A one-dimensional analysis of the Taylor impact test [4] has been used to estimate the quasi-static stress for several different alloys. One criticism of this work was the use of Taylor cylinder test data to estimate the quasi-static true stress/true strain compression diagram. The one-dimensional theory does accommodate this estimate. The purpose of this paper is to demonstrate that this process leads to acceptable results by analyzing a series of high, medium, and low strength materials.

Response spectra of earthquakes on very soft clay

1964 ◽  
Vol 54 (3) ◽  
pp. 855-866
Author(s):  
J. I. Bustamante
Keyword(s):  
Mexico City ◽  
Soft Clay ◽  
Response Spectra ◽  
Wave Reflections ◽  
General Shape ◽  
Dimensional Theory ◽  
Multiple Wave ◽  
One Dimensional ◽  
Velocity Spectra ◽  
The One

Abstract The response spectra of two strong and two mild earthquakes recorded on the thick lacustrine formation of Mexico City in 1961 and 1962 are presented. The velocity spectra of the two strong ones are compared with studies made independently by Jennings. Discrepancies there-with are explained in terms of wave reflections. A criterion to simplify data reduction and spectrum computations is supported by these comparisons. Velocity and pseudovelocity spectra are practically alike. The period corresponding to the maximum peak and the general shape of these curves agree closely with those predicted applying the one-dimensional theory of multiple wave reflections to the formations in question.

INTRODUCING OF INTERNAL VISCOUS FRICTION IN EQUATIONS OF BEAM OSCILLATION AS LONG RECTANGULAR STRIP

2021 ◽  
pp. 54-58
Author(s):  
E.M. Zveriaev ◽  
Keyword(s):  
Stokes Equations ◽  
Asymptotic Series ◽  
Viscous Friction ◽  
Theory Of Elasticity ◽  
Navier Stokes ◽  
Dimensional Theory ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One ◽  
Beam Oscillation

Abstract. On the base of the method of simple iterations generalising methods of semi-inverse one of Saint-Venant, Reissner and Timoshenko the one-dimensional theory is constructed using the example of dynamic equations of a plane problem of elasticity theory for a long elastic strip. The resolving equation of that one-dimensional theory coincides with the equation of beam vibrations. The other problems with unknowns are determined without integration by direct calculations. In the initial equations of the theory of elasticity the terms corresponding to the viscous friction in the Navier-Stokes equations are introduced. The asymptotic characteristics of the unknowns obtained by the method of simple iterations allow to search for a solution in the form of expansions of the unknowns into asymptotic series. The resolving equation contains a term that depends on the coefficient of viscous friction.

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