H.N. Abramson - The dynamic behavior of liquids in moving containers. With applications to space vehicle technology (798543), страница 40
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This istrue because the natural frequency of a givenmode of the structure is inversely proportionalto the characteristic length, whereas the naturalfrequency of any particular mode of the sloshingpropellants is inversely proportional to thesquare root of the characteristic length. Forexample, on a %-scale replica model, the frequencies of the model structure are nine timesas high as those of the prototype, whereas thefrequencies of model propellants are only threetimes as high as the frequencies of the prototypepropellants. Thus the struc ture/propellant frequency ratio, which should be the same onmodel and prototype for similarity, would differby a factor of 3.
Among the ways of overcoming this problem, such as testing the model in ahigher acceleration field (e.g., on the end of acentrifuge) or constructing the model of materials having a lower modulus of elasticity,none have proven very satisfactory. Fortunately, the effects of coupling of the free surfacepropellant sloshing modes with the structuralmodes have not proven to be of primary significance, and the general practice to date has beento select model fluids primarily to simulateprototype propellant masses-Freons to simulate liquid oxygen and nitrogen tetraoxide,naphthas to simulate hydrazine, polystyreneballs to simulate liquid hydrogen.
Frequentlywater can be used, with appropriate allowancesor r-or-reciion Ittctors, to achieve satisfactorysimulation of propellant masses other than forliquid hydrogen. The reader is reminded thatimpurities associated with all of these fluids maybe highly corrosive to aluminum and magnesium alloys, and that the corrosive action isparticularly important because of the thin gagesof materials used and the fact that the tanks areModel Support SystemsFloorFIGURE 5.36.-Horizontalsupport systems for launchvehicles.186THE DYNAMIC BEHAVIOR OF LIQUIDSmaximize the response of the structure in themode of interest. However, if the response ofthe vehicle indicates coupling of other modes,such coupling can be minimized by mountingthe exciter a t a node point of the mode producing the undesired coupling effect..In general, the support cables should bemade of elastic shock cord, but the results ofmany tests of small solid-propellant rocketvehicles a t the Langley Research Center indicate that steel cables can be used successfullyif properly adjusted.
In most cases, a tu-opoint support is adequate for such vehicles, thelocation of these supports being adjusted tocoincide with nodal points of the mode beingexcited.In some cases, particularly those involvingvehicles containing liquid propellants and thinpressurized shells, it is necessary to orient thevehicle vertically to properly simulate theeffects of the earth's gravitational field on thedynamics of the vehicle-propellant system.Herr (ref. 5.41) has studied this problem and hasdeveloped two unique and very effectivesupportsystems, which are shown in figure 5.37.
Bothof these systems closely duplicate the free-freeboundary conditions for such vehicles.The first of these vertical support systems isreferred to as a high-bay harness. The weightof the vehicle is carried by two support cableswhich are attached to the bottom of the vehicleand to the overhead support structure. Stability is achieved by t ~ v ohorizontal restrainingcables tied between the support cable and theperiphery of the vehicle a t some point, forexample, above the vehicle's center of gravity.This support system has essentially tu-o degreesof freedom in the plane normal to the cables:translation as a pendulum and pitching.
I nterms of the dimensions shown on the figure,the stiffness, and thus the frequency, of thepitching mode can be controlled by separationof the points where the support cables fastento the rigid support structure. The vehicle willstand erect ifand the frequency of the pitching mode \\-illapproach zero asThis support system was used successfully onthe )$scale SA-1 and the %o-scale Saturn Vdynamic models studied a t the LangleyResearch Center.I n some instances involving the tests of verylarge dynamic models or full-scale launchvehicle structures, it may be difficult to providean overhead rigid support structure as necessaryfor the high-bay harness. In such cases, thelow-bay harness, though slightly more complicated, is preferable and is being used for thest.ructura1 dynamics studies of the full-scaleThor-Agena launch vehicle now under studya t Langley.
As mas the case for the high-bayharness, the weight of the vehicle is carried bytwo support cables. Hov-ever, in this case,the support cables may be much shorter thanthe length of the vehicle. The vehicle is helderect by controlling the tensions in the restraining cables by means of turnbuckles, and thecondition for neutral stability, and hence, zerofrequency in pitch, is (fig. 5.37)Although i t is still necessary to have somesupport structure near the t,op of the vehicle,this structure can be relatively light, since it'need support only a small fraction of the weightof the vehicle.Model of Saturn SA-1Because of the complex nature of the clusteredst,ructure of the Saturn SA-1, and the urgent,need for experimental data ttoguide the selectionof concepts and assumptions for structuralanalysis, the Langley Research Center construct.ed and tested a %-scale dynamic modelof the SA-1 vehicle (refs. 5.43 through 5.46).The model, supported in the vibration testingtower, is shown in figure 5.38, and some of thedetails of construction and test apparatus areshown in figure 5.39.
The extent to which thefull-scale structure is duplicated in the modelis indicated by figure 5.40. The model wastested while supported in both the high-bay115-Scale DynamicSIMULATION AND EXPERIMENTAL TECHNIQUESharness (fig. 5.37) and with an eight-cablesupport system which simulated the full-scalesupport system (ref. 5.44).
The propellantmasses were simulated with water. The experimen tal vibration characteris tics obtainedon the model are compared with the results ofthe full-scale tests, which were conducted atthe Marshall Space Flight Center (ref. 5.45).On the basis of this comparison, the authorsdrew the following conclusions:(1) The model and full-scale, first-bendingmode frequency parameters are in good agreement (within 6 percent) when the rigid-body,suspension-system rocking frequency parameters are in agreement. The frequency parameters of the model in the first cluster mode, thesecond cluster mode, and the second bendingmode are approlrimately 10 percent below thecorresponding full-scale frequency parameters.(2) For most of the modes, the damping ofthe model is of the same order of magnitude ast,he damping of the full-scale Saturn.(3) The mode shapes of the model in the firstbending, first-clusterland second-c1uster modes187FIC~(IE5.38.-1/5-scaIe dynamic model of Satum SA-1suspended in vibration-testing tower.Fixed oullevs .LC-4High bay harnessVehicle will standerect ifa>f( b cel--e)+bLow bay harnessVehicle will standerect ifFIGURE5.39.-Outrigger-barrel area of 115-scale dynamicmodel of Saturn SA-1.WbT>F 8 ( p )FIGURE j.37.-verticalsupport systems forvehicles (ref.
5.41).launchare in agreement with the correspondingfull-scale mode shapes. Significant differencesbetween the model and full-scale, second-bending-188THE DYNAMIC BEHAVIOR OF LIQUIDSModelFull scaleFIGURE5.40.-Saturnmode shapes are believed to be caused by astructural simplification made in the secondstage structure of the model.(4) Both model and full-scale vehicles exhibitu nonlinearity of the first-bending-mode response characterized by a decrease of resontintfrequency with increase of vibration amplitude.For the range of amplitudes inrestigttted withthe model, the variation of frequency was approximately the same as the rnriation causedby suspension-system stiffness chnnges.115-Scale Dynamic Model of TitanIllPartly as n ~kesultof the successful demonstration of the vtllue of n dy~itimic nod el instudies of tlie structurtil dynnrnics of theSnturrl SA-I luundi vehicle, the -4ir Forceawarded 11 contriict to llcirtin-Den\-el. to construct and test H );-scale dpnnmic model of theSA-1 structural details.Titan I11 launch vehicle.
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