Radial vibrations of an infinite medium with a cylindrical cavity

1963 ◽  
Vol 14 (2) ◽  
pp. 166-169 ◽  
Author(s):  
Václav Vodička
Keyword(s):  
Cylindrical Cavity ◽  
Infinite Medium ◽  
Radial Vibrations

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

Response of Cylindrical Cavity to Traveling Load in Bore

1974 ◽  
Vol 41 (3) ◽  
pp. 800-801
Author(s):  
M. Kojima
Keyword(s):  
Fourier Transform ◽  
Dynamic Response ◽  
Stress Analysis ◽  
Cylindrical Cavity ◽  
Loading Condition ◽  
Infinite Medium ◽  
Transient Solution ◽  
The Past ◽  
The Fourier Transform ◽  
The Relationship

Stress analysis was carried out on a cylindrical cavity in an infinite medium. The normal tractions, which act along the circumference of the bore, rotate continuously or change their rotating directions at t = 0. In this analysis, the Fourier-transform technique according to the theory of distributions was employed to investigate the relationship between the loading condition of traveling traction and the dynamic response. The theory of distributions verified the past solutions and in this analysis it also revealed the possibility of some transient solution.

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