Vibrations of a rotating rigid body with a cavity partly filled with an arbitrary viscous liquid

1973 ◽  
Vol 9 (8) ◽  
pp. 888-891 ◽  
Author(s):  
I. M. Daich ◽  
L. S. Kazhdan
Keyword(s):  
Rigid Body ◽  
Viscous Liquid

scholarly journals Inertial motions of a rigid body with a cavity filled with a viscous liquid

2013 ◽  
Vol 341 (11-12) ◽  
pp. 760-765 ◽  
Author(s):  
Giovanni P. Galdi ◽  
Giusy Mazzone ◽  
Paolo Zunino
Keyword(s):  
Rigid Body ◽  
Viscous Liquid

Mitigation of Rocking and Sliding Motion of a Free-Standing Structure Subjected to Base Excitation Using Coaxial Circular Cylinders Containing Highly Viscous Liquid in Annular Spaces

2019 ◽  
Author(s):  
Atsuhiko Shintani ◽  
Tomohiro Ito ◽  
Chihiro Nakagawa
Keyword(s):  
Rigid Body ◽  
Viscous Liquid ◽  
Analytical Model ◽  
Circular Cylinders ◽  
Base Excitation ◽  
Free Standing ◽  
Seismic Input ◽  
Sliding Motion ◽  
Standing Structure ◽  
Rocking Motion

Abstract In this study, the effectiveness of coaxial circular cylinders containing a highly viscous liquid in annular spaces for reduction of rocking motion of a free-standing structure is investigated both analytically and experimentally. First, an analytical model of coupled rocking and sliding motions of a free-standing structure, including the coaxial circular cylinders, subjected to seismic input was derived. The free-standing structure was modeled as a free-standing rigid body. The cylinders were attached to the bottom of the rigid body as a damping device. We then experimentally derived the friction coefficients, inertia moments, and a damping coefficient in the rotating direction. Furthermore, using these parameters, the effectiveness of this system in suppressing the rocking motion is investigated analytically. The proposed method was determined to be very effective in suppressing the rocking motion of a rigid body subjected to a seismic input by the experiment.

On the motion of a rigid body with a cavity filled with a viscous liquid

2012 ◽  
Vol 142 (2) ◽  
pp. 391-423 ◽  
Author(s):  
Ana L. Silvestre ◽  
Takéo Takahashi
Keyword(s):  
Rigid Body ◽  
Viscous Liquid ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Mild Solutions ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Coupled System ◽  
Analytic Approach ◽  
Navier Stokes

We study the motion of a rigid body with a cavity filled with a viscous liquid. The main objective is to investigate the well-posedness of the coupled system formed by the Navier–Stokes equations describing the motion of the fluid and the ordinary differential equations for the motion of the rigid part. To this end, appropriate function spaces and operators are introduced and analysed by considering a completely general three-dimensional bounded domain. We prove the existence of weak solutions using the Galerkin method. In particular, we show that if the initial velocity is orthogonal, in a certain sense, to all rigid velocities, then the velocity of the system decays exponentially to zero as time goes to infinity. Then, following a functional analytic approach inspired by Kato's scheme, we prove the existence and uniqueness of mild solutions. Finally, the functional analytic approach is extended to obtain the existence and uniqueness of strong solutions for regular data.

Rigid-Body Approximations to Turbulent Motion in a Liquid-Filled, Precessing, Spherical Cavity

1972 ◽  
Vol 39 (1) ◽  
pp. 18-24 ◽  
Author(s):  
J. P. Vanyo ◽  
P. W. Likins
Keyword(s):  
Rigid Body ◽  
Viscous Liquid ◽  
Spherical Cavity ◽  
State Energy ◽  
Layer Structure ◽  
Equations Of Motion ◽  
Solid Sphere ◽  
Turbulent Motion ◽  
Rotating Fluid ◽  
Spherical Shells

Rigid-body approximations for turbulent motion in a liquid-filled, spinning and precessing, spherical cavity are presented. The first model assumes the turbulent liquid to spin and precess as a rigid solid sphere coupled to the cavity wall by a thin layer of massless viscous liquid. The second model replaces the layer of massless viscous liquid by a series of n concentric rigid spherical shells. The number and thickness of the shells can be varied so that the interior sphere varies from a negligible diameter to nearly the diameter of the cavity. Although these models do not provide solutions of the fluid equations of motion, they yield steady-state energy dissipation rates that compare favorably with existing experimental data associated with turbulent flow in such a cavity. The models also duplicate several other important features of rotating fluid flow theory. In particular, the motions of the concentric shells exhibit characteristics associated with a classic Ekman layer structure.

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