The free bending vibration of cylindrical tank partially filled with liquid and submerged in water

1990 ◽  
Vol 11 (5) ◽  
pp. 469-477 ◽  
Author(s):  
Zhou Ding
Keyword(s):  
Cylindrical Tank ◽  
Bending Vibration ◽  
Free Bending

FREE BENDING VIBRATION OF A MULTI-STEP ROTOR

1999 ◽  
Vol 224 (4) ◽  
pp. 625-642 ◽  
Author(s):  
O.S. JUN ◽  
J.O. KIM
Keyword(s):  
Bending Vibration ◽  
Free Bending

On the Sloshing of Liquid in a Flexible Tank

1958 ◽  
Vol 25 (2) ◽  
pp. 277-283
Author(s):  
J. W. Miles
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Liquid Surface ◽  
Frequency Equation ◽  
Cylindrical Tank ◽  
Cantilever Bending ◽  
Free Bending ◽  
Kinetic And Potential Energies ◽  
Tank Diameter

Abstract The kinetic and potential energies of an incompressible fluid having a free surface in a cylindrical tank subjected to translation, rotation, and simple bending are derived in the forms 1 2 ∑ i ∑ j m i j q . i q . j and 1 2 ∑ i ∑ j k i j q i q j where the qi (t) are generalized co-ordinates. The results are illustrated by a calculation of the frequency equation for coupled bending and free-surface motions. It is found that if the mass of the empty tank is small compared with that of the liquid and the depth of the liquid is equal to the tank diameter the presence of the free surface increases the bending frequency (relative to that calculated with a plane cap that coincides with the liquid surface and is normal to the axis of the cylinder) by about 5 per cent for cantilever bending oscillations and 27 per cent for free-free bending oscillations.

K-0642 Measurement of Young's Modulus of Coating Layer using Free Bending Vibration Method

2001 ◽  
Vol I.01.1 (0) ◽  
pp. 279-280
Author(s):  
Hiroshi KASHIMA ◽  
Masayuki ARAI ◽  
Uichi IWATA ◽  
Toshio SAKUMA ◽  
Hirotsugu INOUE ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Coating Layer ◽  
Young's Modulus ◽  
Bending Vibration ◽  
Vibration Method ◽  
Free Bending
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