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 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.

Experimental and Theoretical Studies of Liquid Sloshing at Simulated Low Gravity

1967 ◽  
Vol 34 (3) ◽  
pp. 555-562 ◽  
Author(s):  
F. T. Dodge ◽  
L. R. Garza
Keyword(s):  
Natural Frequency ◽  
Mechanical Model ◽  
Small Diameter ◽  
Bond Number ◽  
Liquid Sloshing ◽  
Theoretical Studies ◽  
Low Gravity ◽  
Equivalent Mechanical Model ◽  
Experimental And Theoretical Studies ◽  
Experimental Comparisons

Analyses and experimental comparisons are given for liquid sloshing in a rigid cylindrical tank under conditions of moderately small axial accelerations; in particular, the theory is valid for Bond numbers larger than 10. The analytical results are put in the form of an equivalent mechanical model, and it is shown that the sloshing mass and the natural frequency of the first mode, for a liquid having a 0 deg contact angle at the tank walls, are smaller than for high-g conditions. The experimental data, obtained by using several small-diameter tanks and three different liquids, are compared to the predictions of the mechanical model; good correlation is found in most cases for the sloshing forces and natural frequency as a function of Bond number.

scholarly journals Analysis of connections and restrictions occurring due to the oscillations of vibrating screen working member and cantilevered screen deck

2020 ◽  
pp. 97-104
Author(s):  
Arkadii V. Iudin ◽  
◽  
Viktor S. Shestakov ◽  
Keyword(s):  
Numerical Simulation ◽  
Mineral Resources ◽  
Oscillatory System ◽  
Operating Mode ◽  
Natural Oscillation ◽  
Forced Oscillations ◽  
Design Stage ◽  
Mass System ◽  
Vibrating Screen ◽  
Wide Range

Research relevance is due to the need of mining companies in a more complete extraction of mineral resources, reduction of crude minerals losses, and extension of deposits’ life. Some enterprises face the problem of complicated high-quality separation of hard-to-screen rock mass. Screen which are common in the industry often become clogged causing decline in the effectiveness of screening. Research aim is to determine the links, build resonant curves and analyze the amplitude oscillations of the working member and cantilevered bars of the screen deck using numerical simulation. Methodology includes the theoretical study of the dual mass oscillatory system with the use of numerical simulation. Results. The motion of the vibrating screen with circular oscillations of the working member, which includes the screen deck of a cascade type with cantilevered bars, is regarded as oscillation of a dual mass system. The amplitudes of oscillations of both masses make in-phase and anti-phase movements relative to the driving force of the drive. The analysis showed that the amplitudes of the working member are practically independent of the screen deck parameters, and bars oscillation amplitudes vary over a wide range. The expressions are given calculating the parameters of cantilevered bars and the values of the initial data of the GIT-51 screen. Resonance curves of amplitude and frequency relations are constructed. The conditions are established under which the oscillation amplitudes of the cantilevered bars take on hyperadmissible values; it is shown that for a particular oscillating system there is a transitional resonance value. Summary. The natural oscillation frequency ratio ranges are established of the entire system with the frequency of forced oscillations in which the oscillation amplitudes of cantilevered bars reach the specified parameters. It is shown that by changing the screen deck parameters at the design stage, it is possible to adjust the inter-frequency range and establish the operating mode of the screen.

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.

DYNAMIC PROPERTIES OF A SYMMETRICALLY CONSERVATIVE TWO-MASS SYSTEM

2013 ◽  
Vol 23 (03) ◽  
pp. 1350039
Author(s):  
CHUNRUI ZHANG ◽  
BAODONG ZHENG
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Numerical Simulations ◽  
Dynamic Properties ◽  
Spatiotemporal Patterns ◽  
Hopf Bifurcations ◽  
Mass System ◽  
Numerical Examples ◽  
Functional Differential ◽  
Bifurcating Periodic Solution

A symmetrically conservative two-mass system with delay is considered. Using the symmetric functional differential equation theories, multiple Hopf bifurcations of the equilibrium at the origin are demonstrated. The existence of multiple branches of bifurcating periodic solution and their spatiotemporal patterns are obtained. Some numerical examples and the corresponding numerical simulations are used to illustrate the effectiveness of the obtained results.

Low-Gravity Sloshing in an Axisymmetrical Container Excited in the Axial Direction

2000 ◽  
Vol 67 (2) ◽  
pp. 344-354 ◽  
Author(s):  
M. Utsumi
Keyword(s):  
Liquid Surface ◽  
Characteristic Root ◽  
Axial Direction ◽  
Bond Number ◽  
Characteristic Functions ◽  
Surface Oscillation ◽  
Low Gravity ◽  
The Past ◽  
Axial Excitation ◽  
Modal Equation

The response of low-gravity propellant sloshing is analyzed for the case where an axisymmetrical container is exposed to axial excitation. Spherical coordinates are used to analytically derive the characteristic functions for an arbitrary axisymmetrical convex container, for which time-consuming and expensive numerical methods have been used in the past. Numerical results show that neglecting the surface tension results in the underestimation of the magnitude of the liquid surface oscillation. The reason for this is explained by the influences of the Bond number and the liquid filling level on the critical value of the coefficient of the excitation term in the modal equation, above which the oscillation is destabilized, and on the characteristic root of the destabilized system. [S0021-8936(00)01502-6]

A Mechanical Model for Low-Gravity Sloshing in an Axisymmetric Tank

2004 ◽  
Vol 71 (5) ◽  
pp. 724-730 ◽  
Author(s):  
M. Utsumi
Keyword(s):  
Mechanical Model ◽  
Bond Number ◽  
Characteristic Functions ◽  
Tank Wall ◽  
Efficient Computation ◽  
Analysis Method ◽  
Low Gravity ◽  
Frequency Responses ◽  
Cost Efficient ◽  
Lateral Excitation

A mechanical model for low-gravity sloshing in an axisymmetric tank is developed using a newly developed slosh analysis method. In this method, spherical coordinates, whose origin is at the top of the cone that is tangent to the tank at the contact line of the meniscus with the tank wall, are used to analytically determine the characteristic functions for an arbitrary axisymmetric tank for which it is customary to resort to numerical methods. By this means, fast and cost-efficient computation can be conducted. Parameters of the mechanical model are determined such that the frequency responses of the resultant force and moment to lateral excitation coincide with those of the actual sloshing system. Influences of the Bond number and the liquid-filling level on the parameters of the mechanical model are examined.

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