Forced Oscillations of a Liquid in a Cylindrical Tank at Low Gravity Environments

1966 ◽  
Vol 39 (6) ◽  
pp. 1267-1267
Author(s):  
Gordon C. K. Yeh
Keyword(s):  
Forced Oscillations ◽  
Cylindrical Tank ◽  
Low Gravity

Free and Forced Oscillations of Magnetic Liquids Under Low-Gravity Conditions

2019 ◽  
Vol 87 (2) ◽  
Author(s):  
Álvaro Romero-Calvo ◽  
Gabriel Cano Gómez ◽  
Elena Castro-Hernández ◽  
Filippo Maggi
Keyword(s):  
Magnetic Fields ◽  
Forced Oscillations ◽  
Applied Mechanics ◽  
Low Gravity ◽  
Linear Dynamics ◽  
Spacecraft Design ◽  
Magnetic Liquids ◽  
Non Linear ◽  
Sloshing Damping

Abstract The sloshing of liquids in microgravity is a relevant problem of applied mechanics with important implications for spacecraft design. A magnetic settling force may be used to avoid the highly non-linear dynamics that characterize these systems. However, this approach is still largely unexplored. This paper presents a quasi-analytical low-gravity sloshing model for magnetic liquids under the action of external inhomogeneous magnetic fields. The problems of free and forced oscillations are solved for axisymmetric geometries and loads by employing a linearized formulation. The model may be of particular interest for the development of magnetic sloshing damping devices in space, whose behavior can be easily predicted and quantified with standard mechanical analogies.

scholarly journals Low-Gravity Fuel Sloshing in an Arbitrary Axisymmetric Rigid Tank

1970 ◽  
Vol 37 (3) ◽  
pp. 828-837 ◽  
Author(s):  
Wen-Hwa Chu
Keyword(s):  
Bond Number ◽  
Forced Oscillations ◽  
Low Gravity ◽  
Mass System ◽  
Numerical Examples ◽  
Galerkin Procedure

Solutions to free and forced oscillations have been found in terms of an auxiliary set of eigenfunctions through the use of a modified Galerkin procedure. The slosh force and moment for an arbitrary axisymmetric rigid tank at arbitrary Bond number have been derived for both pitching and translation, and expressed in terms of characteristics of an equivalent spring-mass system. Numerical examples have been constructed which which compare favorably with available theories and experiments.

Free and Forced Oscillations of a Liquid in an Axisymmetric Tank at Low-Gravity Environments

1967 ◽  
Vol 34 (1) ◽  
pp. 23-28 ◽  
Author(s):  
Gordon C. K. Yeh
Keyword(s):  
Free Vibration ◽  
Velocity Potential ◽  
Translational Motion ◽  
Free Vibration Analysis ◽  
Forced Oscillations ◽  
Mode Shapes ◽  
Low Gravity ◽  
Flat Bottom ◽  
Interface Wave ◽  
Motion Problem

This paper presents a procedure to analyze the free and forced liquid sloshing motions in an axisymmetric tank of arbitrary shape at low-gravity environments. The free-vibration problem is solved by extending the analysis of Satterlee and Reynolds for a circular cylindrical tank with a flat bottom. The forced-motion problem is solved by first expanding the velocity potential, the interface wave height, and the forcing functions in terms of the normal mode shapes obtained in the free-vibration analysis. The solutions hold for any arbitrary horizontal translational motion of the tank.

Three-dimensional large-amplitude drop oscillations: experiments and theoretical analysis

1999 ◽  
Vol 393 ◽  
pp. 309-332 ◽  
Author(s):  
HISAO AZUMA ◽  
SHOICHI YOSHIHARA
Keyword(s):  
Large Amplitude ◽  
Liquid Drop ◽  
Three Dimensional ◽  
Mathieu Equation ◽  
Forced Oscillations ◽  
Variation Principle ◽  
Electrical Excitation ◽  
Low Gravity ◽  
Drop Motion ◽  
The Relationship

Three-dimensional large-amplitude oscillations of a mercury drop were obtained by electrical excitation in low gravity using a drop tower. Multi-lobed (from three to six lobes) and polyhedral (including tetrahedral, hexahedral, octahedral and dodecahedral) oscillations were obtained as well as axisymmetric oscillation patterns. The relationship between the oscillation patterns and their frequencies was obtained, and it was found that polyhedral oscillations are due to the nonlinear interaction of waves.A mathematical model of three-dimensional forced oscillations of a liquid drop is proposed and compared with experimental results. The equations of drop motion are derived by applying the variation principle to the Lagrangian of the drop motion, assuming moderate deformation. The model takes the form of a nonlinear Mathieu equation, which expresses the relationships between deformation amplitude and the driving force's magnitude and frequency.

Oscillations of a vapour cavity in a rotating cylindrical tank

1968 ◽  
Vol 31 (2) ◽  
pp. 249-271
Author(s):  
Sui-Kwong P. Pao ◽  
J. Siekmann
Keyword(s):  
Differential Equation ◽  
Large Scale ◽  
Equations Of Motion ◽  
Angular Speed ◽  
Forced Oscillations ◽  
Infinite Length ◽  
Elliptic Type ◽  
Cylindrical Tank ◽  
Linearized Stability ◽  
Small Force

The oscillations of a curved interface are considered, neglecting the effects of gravity. The system under consideration consists of a right, circular, cylindrical tank of finite length, partially filled with an inviscid, incompressible, wetting liquid. When the container spins about its axis of revolution, the large-scale vapour cavity takes an elongated spheroid-like shape, symmetric about the axis of rotation. The fluid—vapour interface will oscillate about the equilibrium configuration if disturbing forces are present. The case where the vapour cavity touches the walls of the tank is not included in this investigation.The equations of motion are linearized. However, the resulting eigenvalue problem is non-linear. Surface tension and rotation are taken into account only to the extent allowed by a linearized stability theory.The self-sustained oscillations are governed by a partial differential equation of elliptic type, the field equation of the perturbation pressure. According to the results obtained from theory, all eigenfrequencies for this case are greater than twice the angular speed of the tank. The first two eigenfrequencies can be computed with high accuracy. The relation between the bubble shape and the eigen-frequency is shown in a graph for a specific example.The governing differential equation is hyperbolic for forced oscillations induced by a small force field of constant magnitude and direction in an inertial frame of reference. A solution for this problem exists only in case of a cylindrical tank of infinite length. Discontinuities in the velocity components occur in the flow field. A numerical example has been carried out.

Stable response of low-gravity liquid non-linear sloshing in a circle cylindrical tank

2007 ◽  
Vol 28 (10) ◽  
pp. 1273-1285 ◽  
Author(s):  
Yuan-jun He ◽  
Xing-rui Ma ◽  
Ben-li Wang
Keyword(s):  
Cylindrical Tank ◽  
Low Gravity ◽  
Non Linear

Study of the dynamics of ТПА 350 automatic mill working stand elements

2020 ◽  
Vol 76 (8) ◽  
pp. 830-840
Author(s):  
S. R. Rakhmanov ◽  
V. V. Povorotnii
Keyword(s):  
Mechanical System ◽  
Dynamic Model ◽  
Maximum Amplitude ◽  
Calculation Scheme ◽  
Dynamic Loads ◽  
Forced Oscillations ◽  
Mass Model ◽  
Automatic Mill ◽  
Hollow Billet ◽  
Oscillation Movement

To form a necessary geometry of a hollow billet to be rolled at a pipe rolling line, stable dynamics of the base equipment of the automatic mill working stand has a practical meaning. Among the forces, acting on its parts and elements, significant by value short-time dynamic loads are the least studied phenomena. These dynamic loads arise during transient interaction of the hollow billet, rollers, mandrel and other mill parts at the forced grip of the hollow billet. Basing of the calculation scheme and dynamic model of the mechanical system of the ТПА 350 automatic mill working stand was accomplished. A mathematical model of dynamics of the system “hollow billet (pipe) – working stand” within accepted calculation scheme and dynamic model of the mechanical system elaborated. Influence of technological load of the rolled hollow billet variation in time was accounted, as well as variation of the mechanical system mass, and rigidity of the ТПА 350 automatic mill working stand. Differential equations of oscillation movement for four-mass model of forked sub-systems of the automatic mill working stand were made up, results of their digital calculation quoted. Dynamic displacement of the stand elements in the inter-roller gap obtained, which enabled to estimate the results of amplitude and frequency characteristics of the branches of the mill rollers setting. It was defined by calculation, that the maximum amplitude of the forced oscillations of elements of the ТПА 350 automatic mill working stand within the inter-roller gap does not exceed 2 mm. It is much higher than the accepted value of adjusting parameters of the deformation center of the ТПА 350 automatic mill. A scheme of comprehensive modernization of the rollers setting in the ТПА 350 automatic mill working stand was proposed. It was shown, that increase of rigidity of rollers setting in the ТПА 350 automatic mill working stand enables to stabilize the amplitude of forced oscillations of the working stand elements within the inter-rollers gap and considerably decrease the induced nonuniform hollow billet wall thickness and increase quality of the rolled pipes at ТПА 350.

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