Coupling dynamic analysis of spacecraft with multiple cylindrical tanks and flexible appendages

This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks, and a number of flexible appendages. Firstly, the carrier potential function equations of liquid in the tanks are deduced according to the wall boundary conditions. Through employ- ing the Fourier-Bessel series expansion method, the dynamic boundaries conditions on a curved free-surface under a low-gravity environment are transformed to general simple differential equations and the rigid-liquid coupled sloshing dynamic state equations of liquid in tanks are obtained. The state vectors of rigid-liquid coupled equations are composed with the modal coordinates of the relative potential func- tion and the modal coordinates of wave height. Based on the B ernoulli-Euler beam theory and the D＇Alembert＇s prin- ciple, the rigid-flexible coupled dynamic state equations of flexible appendages are directly derived, and the coordi- nate transform matrixes of maneuvering flexible appendages are precisely computed as time-varying. Then, the cou- pling dynamics state equations of the overall system of the spacecraft are modularly built by means of the Lagrange＇s equations in terms of quasi-coordinates. Lastly, the cou-piing dynamic performances of a typical complex spacecraft are studied. The availability and reliability of the presented method are also confirmed.

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

Under pitch excitation, the sloshing of liquid in circular cylindrical tank includes planar motion, rotary motion and rotary motion inside planar motion. The boundaries between stable motion and unstable motion depend on the radius of the tank, the liquid height, the gravitational intension, the surface tensor and the sloshing damping. In this article, the differential equations of nonlinear sloshing are built first. And by variational principle, the Lagrange function of liquid pressure is constructed in volume intergration form. Then the velocity potential function is expanded in series by wave height function at the free surface. The nonlinear equations with kinematics and dynamics free surface boundary conditions through variation are derived. At last, these equations are solved by multiple-scales method. The influence of Bond number on the global stable response of nonlinear liquid sloshing in circular cylinder tank is analyzed in detail. The result indicates that variation of amplitude frequency response characteristics of the system with Bond, jump, lag and other nonlinear phenomena of liquid sloshing are investigated.

THE FREE BENDING VIBRATION OF CYLINDRICAL TANK PARTIALLY FILLED WITH-LIQUID AND SUBMERGED IN WATER

This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode shape functions and inherent frequencies are deduced. The results can be gained by means of computer. The analysis shows that the effect of liquid and water on vibration of cylindrical tank is respectively equivalent to a generalized distributive mass attached to the tank.

Multidimensional modal analysis of liquid nonlinear sloshing in right circular cylindrical tank

The multidimensional modal theory proposed by Faltinsen, et al. （2000） is applied to solve liquid nonlinear free sloshing in right circular cylindrical tank for the first time. After selecting the leading modes and fixing the order of magnitudes based on the Narimanov-Moiseev third order asymptotic hypothesis, the general infinite dimensional modal system is reduced to a five dimensional asymptotic modal system （the system of second order nonlinear ordinary differential equations coupling the generalized time dependent coordinates of free surface wave elevation）. The numerical integrations of this modal system discover most important nonlinear phenomena, which agree well with both pervious analytic theories and experimental observations. The results indicate that the multidimensional modal method is a very good tool for solving liquid nonlinear sloshing dynamics and will be developed to investigate more complex sloshing problem in our following work.

Dynamic Response of A Group of Cylindrical Storage Tanks with Baffles Considering the Effect of Soil Foundation

The sloshing in a group of rigid cylindrical tanks with baffles and on soil foundation under horizontal excitation is studied analytically.The solutions for the velocity potential are derived out by the liquid subdomain method.Equivalent models with mass-spring oscillators are established to replace continuous fluid.Combined with the least square technique,Chebyshev polynomials are employed to fit horizontal,rocking and horizontal-rocking coupling impedances of soil,respectively.A lumped parameter model for impedance is presented to describe the effects of soil on tank structures.A mechanical model for the soil-foundation-tank-liquid-baffle system with small amount of calculation and high accuracy is proposed using the substructure technique.The analytical solutions are in comparison with data from reported literature and numerical codes to validate the effectiveness and correctness of the model.Detailed dynamic properties and seismic responses of the soil-tank system are given for the baffle number,size and location as well as soil parameter.

Experimental Investigation on the Effect of Seal Presence on the Behavior of Double-Deck Floating Roofs in Cylindrical Steel Storage Tanks

Liquid storage,particularly oil and petrochemical products which are considered hazardous liquid,are an important part of the oil industry.Thin-walled vertical cylindrical steel storage tanks are widely used in recent years.Due to high sensitivity of these structures in an earthquake and other external excitations may lead to catastrophic consequences.For instance,huge economic losses,environmental damages,and casualities,many studies have been done about these structures.past studies showed that liquid storage tanks,equipped with a floating roof,are potentially vulnerable while subjected to seismic loads and earthquake has been considered as one of the most destructive natural hazards.The reason is that such tanks are made of two separated parts(shell and roof)which each may have its own responses;sometimes causing resonance phenomenon and so that,roof movements,rooffluid interaction,roof-shell interaction,and also the way they are attached should still be investigated.Experimental tests of floating roof’s vertical fluctuation was performed in a full-scale reservoir tank and assessing of the results demonstrated that presence of a seal between floating roof and shell plate can significantly increase damping ratio in liquid sloshing and also suppress the roof`s vertical displacements.In other words,seal can control a floating roof and make it stop moving vertically over few cycles.

The Research Application of 3D Laser Scanning Technology in the Deformation Detection of Large Cylindrical Oil Tank

In order to ensure the safety in using a large cylindrical storage tank,it is necessary to regularly detect its defonnatioii.The traditional total station method has high accuracy in determining the deformation,however,it has a low measxirement efficiency.Long-term observation means,there are more risks in the petrochemical plant,therefore,this paper proposes the usage of the 3D laser scanner,replacing the traditional total station to determine the defbnnation of a large cylindrical storage tank.The Matlab program,is compiled to calculate the point cloud data,while the tank deformation is analyzed from two different points which are,the local concave convex degree and the ovality degree.It is concluded that,the difference between the data obtained by 3D laser scanning,and total station is within the range of oil tank deformation limit,therefore,3D laser scanner can be used for oil tank deformation detection.

Characteristic analysis of liquid forced nonlinear sloshing under low-gravity

Under low gravity,the Lagrange equations in the form of volume integration of pressure of nonlinear liquid sloshing were built by variational principle. Based on this,the analytical solution of nonlinear liquid sloshing in pitching tank could be investigated. Then the velocity potential function was expanded in series by wave height function at the free surface so that the nonlinear equations with kinematics and dynamics free surface boundary conditions were derived. Finally,these nonlinear equations were investigated analytically by the multiple scales method. The result indicates that the system's amplitude-frequency response changes from ‘soft-spring’ to ‘hard-spring’ in the planar motion with the decreasing of the Bond number,while it changes from ‘hard-spring’ to ‘soft-spring’ in the rotary motion.