Nonlinear motion equations for a Non-Newtonian incompressible fluid in an orthogonal coordinate system

1973 ◽  
Vol 12 (2) ◽  
pp. 212-216 ◽  
Author(s):  
M. H. Cobble ◽  
P. R. Smith ◽  
G. P. Mulholland
Keyword(s):  
Incompressible Fluid ◽  
Coordinate System ◽  
Motion Equations ◽  
Orthogonal Coordinate System ◽  
Nonlinear Motion

Three‐component sonde orientation in a deviated well

Geophysics ◽  
1990 ◽  
Vol 55 (10) ◽  
pp. 1386-1388 ◽  
Author(s):  
M. Becquey ◽  
M. Dubesset
Keyword(s):  
Hydraulic Fracturing ◽  
Coordinate System ◽  
Vertical Plane ◽  
Vertical Axis ◽  
Horizontal Axis ◽  
Orthogonal Coordinate System ◽  
Coordinate Rotation ◽  
Orthogonal Components ◽  
Particle Velocities

In well seismics, when operating with a three‐component tool, particle velocities are measured in the sonde coordinate system but are often needed in other systems (e.g., source‐bound or geographic). When the well is vertical, a change from the three orthogonal components of the sonde to another orthogonal coordinate system can be performed through one rotation around the vertical axis and, if necessary, another one around a horizontal axis (Hardage, 1983). If the well is deviated, the change of coordinate system remains easy in the case when the source is located at the vertical of the sonde, or in the case when the source stands in the vertical plane defined by the local well axis. In the general case (offset VSPs or walkaways) or when looking for unknown sources (such as microseismic emissions induced by hydraulic fracturing), coordinate rotation may still be performed, provided that we first get back to a situation in which one of the axes is vertical.

scholarly journals Geometric characteristics of the deformation state of the shells with orthogonal coordinate system of the middle surfaces

2020 ◽  
Vol 16 (1) ◽  
pp. 38-44
Author(s):  
Vyacheslav N. Ivanov ◽  
Alisa A. Shmeleva
Keyword(s):  
Differential Geometry ◽  
Coordinate System ◽  
Thin Shell ◽  
Tensor Analysis ◽  
Vector Analysis ◽  
Thin Shells ◽  
Orthogonal Coordinate System ◽  
Deformation State ◽  
The Common ◽  
To Receive

The aim of this work is to receive the geometrical equations of strains of shells at the common orthogonal not conjugated coordinate system. At the most articles, textbooks and monographs on the theory and analysis of the thin shell there are considered the shells the coordinate system of which is given at the lines of main curvatures. Derivation of the geometric equations of the deformed state of the thin shells in the lines of main curvatures is given, specifically, at monographs of the theory of the thin shells of V.V. Novozhilov, K.F. Chernih, A.P. Filin and other Russian and foreign scientists. The standard methods of mathematic analyses, vector analysis and differential geometry are used to receive them. The method of tensor analysis is used for receiving the common equations of deformation of non orthogonal coordinate system of the middle shell surface of thin shell. The equations of deformation of the shells in common orthogonal coordinate system (not in the lines of main curvatures) are received on the base of this equation. Derivation of the geometric equations of deformations of thin shells in orthogonal not conjugated coordinate system on the base of differential geometry and vector analysis (without using of tensor analysis) is given at the article. This access may be used at textbooks as far as at most technical institutes the base of tensor analysis is not given.

Free vibration and response of a variable speed rotating cantilever beam with tip mass

2020 ◽  
pp. 107754632097285
Author(s):  
Li Yun-dong ◽  
Hua-bin Wen ◽  
Wen-Bo Ning
Keyword(s):  
Cantilever Beam ◽  
Nonlinear Model ◽  
The Other ◽  
Dynamical Response ◽  
Variable Speed ◽  
Motion Equations ◽  
Green Strain ◽  
Nonlinear Motion ◽  
Good Consistency ◽  
Tip Mass

The study shows a new nonlinear model of a rotating cantilever beam with tip mass. The nonlinear model is built with considering axial geometric nonlinear and large curvature. On the basis of the nonlinear Green strain–displacement relations, the nonlinear motion equations are derived using the Hamilton principle. Applying the proposed dynamic model, the effect of various parameters on the natural frequency and stability is performed. The angular velocity value of frequency veer is obtained under different parameters. The dynamical response is calculated with variable rotating velocity. The comparison of numerical results shows good consistency with the other literature.

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