H.N. Abramson - The dynamic behavior of liquids in moving containers. With applications to space vehicle technology (798543), страница 39
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Data from tests of thetwo-dimensional plates were utilized in a "striptlieory" technique and integrated to obtain theequivalent damping of a circular ring bnffle.One of the conclusions of this test \vas that thedamping effectiveness of ring baffles in cylindrical tanks can be ndequately predicted fromforce measurements in n t\\-o-dimensional tank,even \\-hen surface effects are large. It isSIMULATION AND EXPERIMENTAL TECHNIQUES183FIGURE5.35.-View of teat cylinders and test setup (ref.
5.39). (a) Cylinder 1; (b) cylinder 2.pertinent to note here that the quasi-empiricalring damping formula developed by Miles(ref. 5.37) \+-asderived by similar application oftwo-dimensional data developed by Keuleganand Carpenter (ref. 5.38). As shown inreference 5.28, the damping predicted by Miles1formula is in close agreement mith that measured for annular ring baffles in cylindrical tanks(see also ch.
4).Vibration Characteristics of Pressurized Thin-WalledCircular Cylinders Partly Filled With LiquidThe results of a study of the effects of a contained fluid on the vibrations of thin-walledpressurized tanks which simulate launch vehicleapplicaiiuiis are presented k, rreferszcc 5.39.The investigation treats empty, partly filled,and full conditions for two tanks, shown infigure 5.35, having ratios of radius to thicknessof 937 and 3000.
The cylinders were closed a tthe top by fiber-glass domes and at the bottomby aluminum cones. The tanks were excitedby an air shaker (the rectangular object show-nin the figure to the left of the tanks) \\-hereintheapplied oscillating force n-as derived by interrupting a jet of air with the teeth of a rotatingdisk. The magnitude of the oscillating forcewas controlled by varying the air pressure tothe jet, and t'he frequency was cont,rolledby thespeed of rotation and the number of teeth on thedisk.
The principal advantages of this type ofshaker are the absence of physical ties or addedmass to the structure, and the fine control of thefrequency and amplitude.Using the test setup shown in figure 5.35, theshaker was placed in the position expected togive maximum response of the cylinder in thedesired mode, and the frequency lvas varieduntil maximum response was obtained. Maximum response was observed by touching thecylinder lightly mith the fingertips while varyingthe freql~enryof t,he applied force.
The mode\\-as then identified by locating the node lineswhich represent positions of little or no radialmotion. In nearly all cases, an esperiencedengineer could readily map out the modeshapes using this technique-the only esceptioribeing in the case of the very thin tank \\-henunpress~wized. In this case, the local imperfections tlnd flexibility necessitated the use of aminiature accelerometer (4 gm) to map out themode shapes.184THE DYNAMIC BEHAVIOR OF LIQUIDSComparison of the experimental and theoretical results for this study showed that theequations derived can be used to adequatelypredict tbe characteristics of pressurized cylinders partly fUed with a liquid.
The resultsalso showed that the damping of tank vibrationmodes for the water-filled tanks was less thanhalf the damping measured \!-hen the tanks wereempty-an important consideration relative tothe response of the shell modes of a launchvehicle to engine acoustic and atmosphericinputs.5.10 VIBRATION TESTS OF DYNAMIC MODELSGeneral Considerations and PhilosophyThe evaluation of mechanical systems isgrounded in the mutually supporting developments of theoretical and experimental analysis,and characterized by continued improvementsin structural efficiency-the capability of agiven weight of material to do a bigger andbetter job.
Improvements in structural efficiency are highlighted in aerospace systemssuch as the turbojet engine, the airplane, therocket engine, and the launch vehicle. Rapidimprovements in material properties and fabrication techniques make new, high-performancee needconfigurations feasible and a c c e n t ~ a t ~thefor adequate methods to predict their behavior.Prediction of the characteristics (naturalfrequencies, mode shapes, and response toknown loads) of complex, highly efficient structures such as those of launch vehicles is essentially a two-part problem involving development,of appropriate equations of motion and assigning correct values to the structural quantitiesinvolved.
The third part of the problem, thatof solving the equations, has been largelyovercome through developments in high-speed,high-capacity computers. Comparisons of thepredicted and measured characteristics ofaerospace structures repeatedly demonstratethe need for experimental tests to generate thedata required for refinements of structuralinputs, and show that accurate predictions ofstructural response are difficult to come byexcept by iterat,ive procedures. Such iterationsinvolve analysis, experiment, and comparisonof results; reexamination of analytical assumptions and concepts, reevaluation of the structural properties, revised calculations and tests,the structuraland new comparisons-untilproperties and st.ructura1behavior are predictedwithin acceptable bounds.
Dynamicists haverecognized for many years that dynamic modelsprovide efficient, versatile, and economicalsources of experimental data necessary foradvancement of the state of the art in structuralanalysis. Applications of dynamic modeltechnology to solution of problems of stabilityand control, flutter, and forced response ofaircraft are well documented in the literatureand, more recently, have been applied to launchvehicles and spacecraft as discussed in thefollowing sections.Replica and Dynamically Similar ModelsDynamic models as applied to research inspace vehicle technology to date have been oftwo types : replica and dynamically similar.A replica model is one which involves reproduction of the details of the structure andmaterials.
I t is achieved by essential duplication of the prototype on a smaller scale; dnlessa scale reference is given, the observer could nottell from a picture of the composite vehicle orany of its components whether it be the modelor prototype. An exact replica model is verydifficult to achieve for obvious practical reasons,but the Saturn V model discussed subsequentlyis a close approximation. Whereas the designof a replica model is simple (achieved by scalingthe numbers on the prototype dranings), itsconstruction may be a very difficult task,necessitating the use of very thin shells andreinforcement structures and new tooling forfabrication. These considerations essentiallylimit the minimum size of such models.Dynamically similar models encompass those~vherein the important dynamic properties,such as mass and stiffness distributions, arereproduced or simulated either by the use ofsinliltir materials and fabrication techniques orby approfirnations t,hereto.
I n essence, ad J-nainicallg similar model, usually referred toas a dyrlanlic model, is one which exhibitscharacteristics which closely represent the185SIMIJLATION AND EXPERIMENTAL TECHNIQUEScounterparts of the prototype in the areas ofimportance relative to the phenomena beingstudied on the prototype. The ?6-scale SaturnSA-1, !&scale Titan 111, and >:,,-scale Saturn Vmodels discussed hereafter are of this type.pressurized. I t has been found necessary tocoat the interior of the tanks, to purify Freon,and to deionize and deactivate water withinhibitors such as sodium chromate.Propellant Simulation in Large Dynamic ModelsIn essentially all cases of interest, the boundary conditions for launch vehicles are essentiallyfree-free, and an equivalent support systemmust be used during dynamic model tests toassure that the natural frequencies, modeshapes, structural damping, and dynamic response of the model represent those which occuron the full-scale vehicle under flight conditions.The fundamental criterion is one of frequencyseparation.
If the frequency of the supportsystem can be made sufficiently low comparedto the natural frequency of t,he lowest frequencynatural mode of interest, say by a factor of 3octaves, the effect of the support system on thestructural characteristics of the model canusually be neglected.
The techniques for supporting various types of dynamic models, andin some cases, full-scale vehicles, are discussedin references 5.40 through 5.42.If the structure of the vehicle is such that itmay be handled as a unit and can be orientedhorizontally, the better approach is usually tosupport it, as shown in figure 5.36. This technique has been used effectively for emptylaunch vehicle stages up to the size of the Thor.In this type of support system, the effect of thesupport is secondary, and if, in the excitation ofthe natural modes of the structure, the supportsare located a t the nodal points, t,heir effect onthe structure is negligible. I t is usually desirable to mount the exciter near an antinode toAs developed in section 5.4, the simulation offuel sloshing is a most difficult task in any modelof a launch vehicle which is adequately scaledand constructed to provide quantitative data ofstructural dynamics of the prototype.
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