Computer Techniques for Use in Ship Hull Vibration Analysis and ...

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❑Several types of computer programsare suitable for this analysis. The systemcan be broken down to a sequence ofmasses connected by springs. This canbe analyzed by a Holzer Table program,the kind developed for torsional vibration,or by a standard finite elementprogram such as ANsYS, MARC, STARDYNE,NASTRAN, SESAN, etc. However, the shafting,“hose distributed weight is severaltimes that of the propeller with its associatedwater inertia, consists of longlengths of constant diameter. Thischaracteristic is encouraging to a programthat represents the shaft as distributedmass and elasticity, and a fewcomputer programs have been developedwhich utilize this property. In such acase the system can be defined with aminimum of input variables, thus savingtime and improving accuracy and reducingthe probability of erroneous inputs.The following appendices taken fromReference (25) indicate that the MaritimeAdministration has a program (Appendix14-1) based upon the Holzer Methodfor determining longitudinal vibrations;that J. J. McMullen has a program(Appendix 14-2) for determining longitudinalvibration “here the sha.ft is model -ed as lumped masses; and that NewportNews has a program (Appendix 14-3) thatcan represent the shaft as a distributedmass system. A Littleton Research programutilizing lumped and distributedmasses and elasticities is described inAppendix 14-4. Reference (26) containsresults of a survey for ship structurecomputer programs made in 1974.Determine Forced Response of MachinerySpace - [Box 1The shafting system is connected inlongitudinal vibration to the machineryspace double bottom through the thrustbearing. Thus, vibrations of the shaftwill be coupled with those in the machineryspace, and vibrations in the machineryspace bottom structure can bestrongly coupled with longitudinal vibrationof the shafting. Although itmight be desirable to model the doublebottom as an anisotropic plate with variableinertias for the same reasons thatthe distributed mass-elasticity procedureis used for the shafting, this typeof model has not been developed, and itis necessary to use finite element modeling.It is desirable that the comp”-ter system that is used be compatiblewith that used for the complete ship.Tf the final ship is to be modeled byfinite element procedures, the same systemshould be used for the machineryspace, which can then be incorporated inthe full model as a substructure. Ifthe complete ship is to be modeled as aTimoshenko beam with sprung masses, anyconvenient finite element model can beused for the machinery space.Determine Forced Response of the shaftinqin the Lateral Direction Assunung aRigid Hull; i.e. , Rigid Fin Support atBearings - [Box 16]The shaft responds laterally to theharmonic force and moment excitationsabout axes normal to the rotational axis.If the lateral natural frequencies ofthe propeller and shaft system coincidewith the blade frequency excitation, theinput to the hull through the bearingscan be strongly amplified. Calculationsof ship response generally show peaksassociated with lateral frequencies ofthe shafting. It is, therefore, desirableto design the shafting system sothat these resonances will not occur atthe normal operating speeds. As withthe longitudinal vibrations, these studiesare successively made on models ofincreasing complexity. The first studiesare applied to the shaft simply supportedat the bearings (either at theforward and after edges or one-third ofthe distance from the rear of the sternbearing ). Since it is known that thebearings are relatively flexible, thismodel will generally give a frequencythat is high so that if the lo”est lateralfrequency is less than, say, 30percent above the full power blade frequency,it will probably be wise to considerrelocating the bearings or modifyingthe shafting to raise the frequency.A finite element computer program issuitable for this analysis. It is alsowssible to use beam programs which includethe effects of hull flexibility.The supporting structures can be modeledby making the supports very stiff orrigid. These programs are discussed inthe next section.Determine the Lateral Responses of theShafting Including the Effects of nullFlexibility - [Box 17]If gyroscopic effects are neglected(they are im~rt.ant for whirling, butrelatively unimportant at blade frequencies)and the supports are of equalstiffness in all directions, the naturalfrequency and response of the shaft willbe the same in all directions. If thestructure is symmetrical about a verticalaxis and gyroscopic effects are neglected,the shaft will have two naturalfrequencies and corresponding modeshapes, one vertical and one horizontal. “If the structure is not symmetrical, thefundamental normal modes will be skewedto the vertical, but at right angles toeach other. The moment restraint at thebearings can have a significant influenceon the shaft frequency. .The amount of structure to includein the stiffness calculation is a matterfor the analyst’s judgement. Theobject is to evaluate the stiffness toa region of a large hull mass. Fox asingle screw ship, this may involve theK-6 +-

structure fmm the after peak bulkheadand up to the steering gear flat. Forshafts supported by struts, it will includethe struts and their backup structure.If the complete hull is analyzedusinu a finite element analvsis [Boxes20 a;d 211, the validity of- the modelingcan be tested.Since the structure supporting theshaft bearings is complicated, the useof finite element methods is the mostfeasible way of determining tbe supportstiffness. The stiffness between theshaft and bearing of a stave bearing canbe quite low if the staves are rubber.Tbe stiffness of an oil film bearing issuch that a bearing force introduces amotion having a component perpendicularto the load.If, as a result of tbe calculationsof shaft response, it is found thatthere are no shaft resonances near theoperating speeds of the ship, the shaftingcan be considered satisfactory forthis level of refinement. Later analysesof the whole ship will confirm itssuitability. If, on the other hand,lateral resonances appear close to theoperating speed, then by changing one ormore of the following, a new propulsionsystem can be developed which has resonancesproperly located:1. The overhang of the propeller beyondthe stern bearing.2. Tbe span between the last two bearingssupporting the propeller shaft.3. The diameter of the propeller shaft.4. The support of the propeller shaftbearing:(a)(b)(c)(d)The skeg and stern tube structurefor a single screw shiphaving a skeg supported bearing.The angles, size, attachmentto the bearing barrel of thearms carrying a strut bearingfor open screw ships.The structure supporting strutarms .Other changes as indicated bythe calculations.Such changes are frequently required,and good judgement, often using analysesof simple models, is required to discoverthe optimum solution rapidly and inexpensively.Appendices 17-1 and 17-2 presentinformation on two computer programsused for.the analysis of transversepropeller shafting vibration.Conduct Superstructure Modal Analysis -[BOX 18]In addition to substr”ct”res of theshafting and machinery spaces, it is desirableto make a study of the superstructureas a subsystem since resonancesin this region are a freguentcause of vibration troubles. Finiteelement methods are generally most suitablefor modeling this structure by consideringit to be attached to a rigidstrength deck. With the high superstructurescommon on container ships and verylong ships, some superstructures vibratefore and aft as a cantilever beam. Onothers the decks vibrate symmetricallywithin the sides, while on still othersthe decks vibrate anti-symmetrically(port up, starboard down) so that thefinite element model should not be toocoarse to suitably represent the complexityof possible modes. Clearly themost suitable programs for these analysesare finite element programs.It may be desirable to make substructuralstudies of other portions ofthe ship such as the rudder born subsystemor systems involving stern crane orelevator carriers. It might also be desirableto combine two or more smallersubsystems. For example, the lateralshaft and substructure subsystem can beconnected to the longitudinal shaft andmachinery space subsystem to form a largercombined subsystem.When the subsystems have been designedso that it is expected that theywill be free of vibration resonances, itis time to make a vibration analysis ofthe complete ship. This analysis of thefull ship fulfills two important functions:1. It checks and confirms the validityof the boundaries assumed for thesubstructures.2. By modelinq the ship as a whole, itis possible, with the proper damping,to predict the vibration levelsin all parts of the ship as afunction of frequency. Comparingthese predictions with establishedacceptable levels allows an assessmentof acceptability of the shipa,ta point in construction wherecorrections and changes to overcomeserious difficulties can be determinedand incorporated in the desiqn.Assemble Model of Entire Ship and DetermineVibration ?unplitudes and StressLevels of the Compl ete Ship - [Boxes 20and 21]Reference (8) indicates that undersome conditions the complete ship may besatisfactorily modeled as a beam structureUslncj a TunosnenKO Beam as a base.K-7

For vertical vibration the ship may bemodeled as parallel beams elasticallyconnected and carrying sprung weights.For lateral vibrations the bending isstrongly coupled with torsion, and so acoupled model is required. Strictlyspeaking, the vertical bending should becoupled with axial vibration of the ship,and this is probably advisable if theblade frequency approaches an estimatedlongitudinal frequency of the ship.Nhere these conditions cannot bemet, it is necessary to model the shipby finite element methods in order toobtain reliable estimates of response.Although heavy vibrations of twiceand three times blade frequency can bemeasured on ships, the methods of analysisthat are presented in this paper arefeasible only for the range of the fundamentalblade frequency, except for unusualcases.As an example of a ship modeled interms of beams, consider Figure 2, anuncoupled vertical vibration model, andFigure 3, a coupled lateral-torsionalvibration model. A finite element modelfor half a shiD (because of svmmetrv.only half need” be represented is siiwnin Figures 4 and 5.For the analysis of structures ascomplex as shown in Figures 2 and 3, thecomputer program GBRP (General BendingResponse Program) developed at the NavalShip Research and Development Center (27)should be used. In the analysis of theship hull, it can treat vertical as wellas coupled lateral-torsional vibration.These capabilities and other features ofthe program are described in Appendix20-1.To define the elastic properties ofthe strwcture, it is necessary to definethe cross-sectional elastic properties.A program and procedure for computingI Y1=1 yzA(Moment of inertia about transverseaxis)(Moment of inertia about verticalaxis )(Product of inertia relative tohorizontal and vertical axes)(Cross-sectionalarea)? (Transverse Coordinate of neutralaxis)y’, z’ (COOrdinates of tbe shear centerof the section)is given in Reference (28). ‘This programcalculate.s the equivalent beam parametersfor the ship section propertiesusing data tabulations obtained fromhull plans by a preestablished orderlyprocedure.U.S. Steel Engineers and Consultants,Inc. , developed a program thatrepresents a ship as a beam on an elasticfoundation. Information on thisprogram is given in Appendix 20-2.Other vibration programs based upn modelingthe hull as beams have been developedby Lloyd’s Registry of Shipping andby Dr. Ing. E. Metzmeier of the InstitutftirSchiffstechnik in Berlin, FederalRepublic of Germany. These programsare briefly described in Appendix 20-3.The factors that enter into thechoice of the number and location of thesubdivisions of the hull structwe areconsidered in Reference (8). The advantageof representing a ship by a beammodel is that the computer analysis ismore direct and more easily interpretedand is considerably less expensive thanthat with a finite element analysis fora structure that is as well defined.Tbe disadvantages are that for many shipvibration problems, particularly wherethe decks are open so that tbe vibrationacross the width of tbe ship is important,the beam representation of theship is inadequate and a finite elementprocess is required for satisfactorymodeling.The use of finite element methodsfor predicting ship vibrations is becomingwidespread. Some organizations havedeveloped finite element programs specificallyfor shiD aDDlicatiOns. Amonclthese sh&ld be m&ti&ed SESAM-69 (AP:pendix 2O-3) developed by Det norskeVeritas, the Norwegian classificationsociety (29), and DASH (Appendix 20-3)developed by the Netherlands Ship ResearchCenter. Bureau Veritas, theFrench classification society, has mademany finite element analyses of shipstructures. They do not supply informationon the characteristics of theirprogram.KXZAKxYAJxz(Shear area constant verticalplane](Shear area constant transverseplane)(Torsional area constant aboutlongitudinal axis )(Vertical coordinateneutral axis)of theThe Electric Boat Division of GeneralDvnamics Corporation develoued andmaintains a finit; element compu~er programGENSAM for use on submarine vibrationproblems. Information on this is 1’presented in Appendix 20-3.Since the cost of developing, maintaining,and updating a large finiteelement computer program is high, it iscommon to apply general purpose computer[-8“L

,I II IFIGURE 4. ELEVATION VIEW OF FINITE ELEMENT MODELFIGURE 5. ROTATED VIEW OF FINITE ELEMENT MODEL.K- 10

14.15,16.17.18.19.20.21.22.23.24,25.S. Tsakonas and W. R. Jacobs, “Documentationof a Computer Programfor the Pressure Distribution Forcesand Moments cm Ship Propellers inHull Wakes, ,,Stevens Institute ofTechnology, Davidson LaboratoryRept. SIT-DL-76-1863 .N. A. Brown, “Periodic PropellerForces in Non-uniform Flow, ‘uMassachusettsInstitute of Technology,Dept. of Naval Architecture and MarineEngineering Rept. 64-7, 1964.0. Frydelund and J. E. Kerwin, ‘,TheDevelopment of Numerical Methodsfor the Comp”taticm of unsteadyPropeller Forces, ,,Symposium onHydrodynamics of Ship and OffshorePropulsion Systems, Det norske Veritas,oslo, Norway, March 1977.M. T. Murray and J. E. T“bbyr“Blade-Rate Force Fluctuations ofa Propeller in Non-Uniform Flow, ,,Admiralty Research Laboratory, ARL/M/P33A, June 1973.P. van Oossanen and J. van der Kooy,‘“Vibratory Hull Forces Induced byCavitating Propellers, ,STrans . RoyalInstitute of Naval Architects,vol. 115, 1973.w. S. Vorusr “A Method for Analyz.ing the Propeller-Induced VibratoryForces Acting on the Surface of aShip Stern, “ Trans. SNAME, vol. 82,1974.M. Yildiz and O. K. Mawardi, “onthe Diffraction of Multiple Fieldsby a Semi-Infinite Rigid Wedge, ,,Journal Acoustical Society of America,vol. 2, ~—No.M. Yildez and O. K. M.?nr?.rdi,~,Dif -fracticm of a Dipole Field by aRigid Cone (Abstract) ,‘uJournalAcoustical Society of wn~vol.32, No. 12, 1960.P. van Oossanen, “Theoretical Predictionof cavitation on proneI -lers,’s Marine Tecimml.og , voi. 14,No.H. Schawanecke, ,,Compari son o fMethods for the Calculation of wakeInduced Propeller Blade ExcitingForces, “ International Towing TankConference, Ottawa, Canada, PaperNo. 13, 1975.“Longitudinal Stiffness of MainThrust Bearing Foundations, ‘uSNAMETechnical and Research Report R-15,Sept. 1972.The National Shipbuilding ResearchProgram - Research on Computer Applicationsto Shipbuilding VII,26..27.28.29.30.31.32.33.34.catalog of Program Abstracts - u.s.Dept. of commerce, Maritime Administration,in cooperation with AvOndaleShipyards, Inc. , May 1975.R. F. Jones, Jr. , “Ship Structures, “Structura~ Mechanics computer Pro-=, Edited by W. Pilkey, et al. ,University of Virginia Press, Charlottesville,1974.M. E. Golden and F. M. Henderson,“An Updated Guide to the Use ofGeneral Bending Response Program(GBRP),‘,Computation and MathematicsDept. Research and DevelopmentRept. 4601, Naval ship Research andDevelopment Center, Bethesda, Md. ,April 1975.R. C. Leibowitz and R. L. Harder,‘Mechanized Computation of Ship Parameters,” David Taylor Model BasinRept. 1841, June 1965.0. Egeland and P. 0. Araldsen,,,sE$m-~g _ A General purpose FiniteXlement Method Program, ‘uComputersand Structures, vol. 4,=41-68, Pergamon Press, 1974.J. E. Kerwin, “Computer Techniquesfor Propeller Blade Section Designs,” International Shipbuilding20, No. 227, JUlyP ‘0’“S. Tsakonas, W. R. Jacobs, and M. R.Ali, ,,Documental ion for the CompleteProgram for tbe PressureField Generated by a Propeller ina Variable Inflow, “ Stevens Instituteof Technology, Davidson LaboratoryRept. 1910, May 1977.R. G. Kline, R. W. Clough, and D.Kavlio, “Propel ler-Excited Vibrations,’,SNAME, Northern CaliforniaLocal Section, March 1971.Lloyd, s Register, Development UnitReport No. 131.S. Hylariades, “DASH, Computersr~gram for Dynamic Analysis OfShip Hull s,” Netherlands Ship ResearchCenter Rept. No. 159/S, NSMBPublication 367, Sept. 1971.K-12

APPENDIX 4-1. LONGITUDINAL VIBBATIONOF SHAFTING, 1Program Developed and Used by LittletonResearch and Engineering CorporationOutputInformationA plot of natural frequency of theshafting system as a function of thestiffness of the thrust bearing and itsfoundation. Alternatively, if thethrust bearing stiffness is known, thevariable may be the foundation stiffness.InputInformation1. Shafting arrangement, diameters,and lengths.2. Propeller mass, diameter, numberof blades, pitch, and developedarea ratio (or mean width ratio) .Basisfor CalculationThe propeller is represented by itsweight and the weight of entrained wateras given by Lewis and Auslaender. Theshaft is represented by a distributedmass and elasticity. The gearing andturbines forward of the thrust bearingare not included.This is a proprietary program notdeveloped for general distribution.APPENDIX 6-1. PROPELLER MEAN ANDVIBBATORY FORCES PROGRAMProgram Developed by Davidson Laboratory,Stevens Institute of Technology,under U.S. Navy contracts; “idely used.OutputInformation1. Steady and time-dependent bladeloading distribution at multiplesof shaft frequency.2. Mean and blade-frequency force andmoment components in coefficientform for:where(a)(b)Thrust/on2d4Torque/pn2d5(c) Transverse force/pn2d4[d) Vertical force/on2d4(e) Transverse bending moment/~n2d5(f) Vertical bending moment/on2d5o = fluid densityn . propeller rpmd = propeller diameter3. Blade bending moments about thepitch line at various radial posi -t+ons and for various orders of excitation.4. Information for the study of cavitationinception.5. Information for tbe study of bladestress analysis which is performedby utilizing the STARDYNE-CDC finiteelement computer program.InputInformation1. The propeller blade geometry.2. The Fourier components of the spatialvariation of the axial and tangentialcomponents of the wake.Basisfor CalculationThe program uses unsteady liftingsurfacetheory and takes into considerationall the relevant propeller qeometryand the spatial nonuniformity of the inflowfield.The program is available throughDavidson Laboratory for $6,000. See Reference(14).APPENDIX 6-2. HAPMONIC FORCES AND MO-NENTS GENERATED BY A PROPELLER IN NON-UNIFORM FLOWProgram Developed and Used by LittletonResearch and Engineering CorporationOutputInformation1. Magnitude and phase of the threecomponents of harmonic propellerforce and the three components ofharmonic propel ler moment.2. The steady vertical and horizontalforces and moments arising fromfirst-order “ake action (thrustoffset) .InputInformation1. Propeller dra”ing.The propeller drawing should showthe fol lowing information: prOpel -ler diameter, hub diameter, rake,number of blades and propeller material;the variation with radius ofchord, skewback, and pitch; propellersections at several radii sho”-inq the variation of thickness alongthe chord. For propellers designedin Europe, the “ariation with radiusof the distance from the referenceline to the leading edge, trailingedge, and point of maximum thicknessis acceptable in place of the variationof chord and skewback.K-13

2. Ship speed and corresponding shaftrpm.3. Wake as measured in a model test.BasisThe results of a harmonic analysisof the measured wake are required.If the harmonic analysis resultsare not available, the mess.”red inflowvelocities specified at severalpoints along the radius and atfrequent PO ints around the circumferenceare acceptable, and a harmonicanalysis will be performed.If a measured wake is not avail.able, it can be inferred from theavailable wakes of other ships.for CalculationsPropeller forces are determined bylifting line theory. This is much lesscomplex than tbe Davidson Laboratorylifting surface theory, but is consideredadequate in view of uncertaintiesin the wake and the wide variation inservice wake due to ship motions andsea action.The main reason for continuing touse the lifting line theory calculationis that it is the basis for the predictionsOf hull pressure and hull force S(see Appendix 7-1) .This is a proprietary proqram notdeveloped for general distribution.APPENDIX 6-3. CALCULATION OF STEADYAND HARNONIC PROPELLER FORCESComputer Program used by tbe AmericanBureau of ShippingOutputInformation1. Mean and blade-frequency ccunponentsof the three forces andthree moments acting on the propeller.2. Time -”aryin.g blade pressure distributionat each wake harmonic .InputInformation1. Propeller blade geometry.2. Fourier coefficients of the spatialvariation of the axial andtangential components of wake.Basisof CalculationThe program employs an extendedversion of unsteady lifting line theoryas developed by Dr. Neal A. BrCIWn atMIT (15). The extension includes theeffects of propeller skew, which werenot treated in the original theory.The results of this program are used aspartial input to the ,,s”rface Force,sK-14program described in Appendix 7-3.APPENDIX 6-4. HARNONIC FoRcEs AND MO_MENTS GENERATED BY A PROPELLER IN NON-UNIFORM FLOWA Computer Program under Development atMassachusetts Institute of Technology byprOfessOr Justin E. Ker”in, Departmentof ocean EngineeringThe program represents the propellerblade by grid points distributedover tbe surface and the wake spatiallydefined (cylindrical coordinates) inthree directions : longitudinal, tangential,and radial. A distribution of ~or.ticity is assumed over the surface, andby successive iteration is refined to becompatible with the boundary of the propellersurface and the laws of hydrodynamics,Kel”in, s theorem, and the Kuttarequirement for flow Continuity at thetrailing edge.This discrete element approach appearsto offer a number of advantages asa starting point for the computation ofunsteady, partially cavitating flo”s:(a) It is capable of yielding accuratepredictions of mean loading, bothat design and off-design conditions.(b) Being a numerical procedure, bladegeometry can be incorporated exactlyso that propellers with larqeskew, rake, and varying pitch distributioncan be accommodated. Thisis considered essential, since itis through the variation of theseparameters that optimum propellerdesigns can be evolved.(c) Since the procedure includes allthree components of induced velocity,there is no particular problemin including tangential and radialwake field components.(d) since no loading mode functions areemployed, the modifications ultimatelyrequired to include the cavitieswould appear to be feasible.Source elements presently includedto represent blade thickness canassume the further role of representingthe cavity volume.(e) A discrete element method lends itselfnaturally to a step-by-stepdomain solution, which is also essentialfor the subsequent incl”-sion of unsteady cavitation.The procedures are still under development,but have been applied to specific cases with good results. See References(16) and (30).I\+-‘!

APPENDIX 6-5. HARMONIC FORCES AND MO-XSNTS GENESATED BY A PROPELLER IN NON-‘~lFORM FLJ3WComputer Program Developed and Used bythe Admiralty Research Laboratory, Teddington, EnglandOutputInformation1. The input data.2. If wakes are given as velocitymeasurements, the harmonic valuesare printed (to the 71 harmonic ).If given as Fourier components,these are listed.3. The contribution to thrust, torque,vertical and horizontal forces, andmoments from each specified radialsection.4. The integrated thr”str torque,horizontal and vertical forces,and moments fox multiples of bladerate harmonics.Input1.2.3.4.5.6.7.8.BasisInformationShaftspeed.Propeller geometry, including skew,chord length, blade pitch angle atspecific radii.Wake, either in Fourier series,amplitude-plus-phase form, or asequally spaced measurements ofwake at the radii where the propellergeometry information isgiven. Only axial or both axialand tangential wakes may be speci -fied.Calculations can be r“n for S“C_cessive skew values.Input radii may vary from 4 to 14.As many as 20 skew configurationsmay be determined.As many as 140 harmonics of theblade frequency forces may be calculated,but generally the numberis limited to 10.As many as 100 wake harmonics and200 wake measurements per radiusmay be input.for CalculationThe calculation of the fluctuatingforces on a propeller falls into threeparts. The first part is the calculationof the variation of the inflow velocityto the blades; the next stageinvolves the calculation of the fluctuatinglift-distribution on a section ofblade associated “ith this fluctuatinginflo”; the final stage is the calcula -tiOn of the propeller forces a“d ~Oment S .The calculation of the fluctuating liftis based on two-dimensional unsteady airfoiltheory. It ignores blade-to-bladeinteraction and the “ariation with radiusof the “ario”s significant parameters .These approximations “ould be “acceptablefor predicting the steady lift, butare acceptable for the unsteady lift,probably overestimating the lift. SeeReference (17).APPENDIx 7-1. CALCULAT1 ON OF HARMONICFORCES AND MONENTS ON THE HULL GENERATEDBY PROPELLER ACTIONProgram Ueveloped and used by LittletonResearch and Engineering CorporationOUtputInformation1. The harmonic hull surface pressureat blade beat frequency generatedby the loaded, noncavitatinq prO -peller in the region of the propeller(generally at grid points correspondingto underwater intersectionsof buttocks and frames within4 diameters of the propeller) .2. By integration of the abo”e, theblade frequency harmonic hullforces and moments acting on thehull because of noncavitating propelleraction.InputInformation1. The computed propeller 1ift distr i-bution along the propeller blade(see Appendix 6-2) .2. The geometry of the propeller.3. The hull coordinates at the pointsof pressure determination.Basisfor CalculationThe free-field pressures (i.e., thepressures that would exist in open waterif the hull “ere not present) are calculatedat each hull grid point due to (1)the loading on the propeller blades (assumedto be concentrated at the forwardquarter point of the blade chord) , (2)the thickness of the propeller blade.The sum of these two pressures, in theirproper phase, is multiplied by 2 to givethe reported pressure cm the hull surface.The pressure from a harmonicallyvarying force having x, y, and z componentsinvolves the distance from thepoint to the location of the force.Substituting steady and harmonic forcesand distances as a function of shaftangle yields values of the pressure.The result ing equations invol”e a serieswhich under certain conditions con”ergesslowly . originally only a fe” termswere developed. More recently the generalterm has been de”eloped, allowingK-15

sufficient terms to assure convergence.This results in pressures that correspondto measured values. The integrationfor blade thickness is similar.If the cavitation volume on the bladecould be defined by a Fourier sexies,the same process could be applied.This has not yet been done.This is a proprietary program notdeveloped for general distribution.See Reference (13).APPENDIX 7-2. CALCULATION OF STEADYAND HARMONIC PRESSURE FIELDS GENERATEDBY A NONCAVITATING PROPELLERProgram Developed by Davidson Laboratory,Stevens Institute of Technology,Under U.S. Navy ContractsOutputInformationThis program furnishes the steadyand harmonic components of the pressurefield qenerated by a none.s.vitatinashi~propelier operati;g in a spatiall~ var~iable inflow.InputInformation1. The propeller blade geometry.2. The Fourier components of the spatialvariation of the axial andtangential components of the wake.3. The spatial location of the pointswhere tbe pressures are desired.2.3.4.5.BasisWakedistribution.Stern lines and coordinates describingthe sectional geometry of approximatelytbe aft one-third ofthe ship.Time-dependent geometry of propellercavitation effects (optional) .Time-varying blade pressure distributionat each wake harmonic (outputfrom program described in Appendix6-3) .of CalculationThis program employs the method presentedby Professor William s. vorvs inReference (19). The conventional procedureof evaluating the hull forces is tointegrate the propeller-generated pressuresover the hull surface. These pressuresare due to diffraction of tbe propeller-inducedwater flow by the hull.The diffraction problem and hence thepressure integration difficulties areavoided in the analysis and computer programby utilizing a special applicationof Green’s Theorem.APPENDIX 14-1. IQNGITUDINAL AND TOR-SIONAL SRAFTING VIBRATIONSProgram Used by Maritime AdministrationNumber and/or Name.,~-g+oz4. The steady and time-dependent bladeloading distribution at multiplesof any shaft frequency as producedby the program described in Appendix6-1.Basisfor CalculationThis program is a continuation ofthe one described in Appendix 6-1 andrequires data generated in that program.It is available through Davidson Laboratoryfor $5,000. See Reference (31).APPENDIX 7-3. mCUUTION oF pROPELLER-INDUCED HULL SURFACE FORCESProgram Developed and Used by ProfessorWilliam S. Vorus (University of Michigan)and tbe American B“rea” of ShippingOutputInformationThis program computes all componentsof tbe hull force and moment atmultiples of tbe propeller blade rates.(In general, the vertical force componentis the only one desired. )InputInformation1. Propeller geometry.K- 16Category (s)..~”~~**ShaftingCalculationsDescriptive Proqram TitleSource**Shaft Vibrational Analysis**Using Holzer MethodActivity**Office of Ship Construction**Maritime &dmini~tratiQn**Washington, D.C.Engineer (s) Name-Code-PhoneProgrammerProgram**Richard Siebert, 721.21, 254-7048**ff&v~~~Status.*prod UctiOnClassificationName-Code-Phone(Security)**Restricted - NAVSEC Program,.+-

ProgramingComputerspecialSpecialLanguage* *~~~~RAw ~“Type Used**~ont=o~,.~o~~**NoneHardware~a~~6600Software/OperatiOnProgram size-Source Deck Cards**~~~Program Size-Object Core Words**c~~oo~o oc~a~ wor~~Average Running Time (Min)Program**1.57Availability,*septe”ber 1970DocumentationProgramStatus**informal - Complete (15 pages)AbstractThis program calculates torsionaland longitudinal critical vibrationfrequencies using the Holzer Method. Itwas originally developed by NAVSEC forthe IBM-7090 and subsequently convertedto the CDC-6600 by the Maritime Administration.Double precision requirementswere eliminated. Input requires handcalculation of all masses, inertias, andstiffness factors for each component inthe turbine-gear-sha ft-propeller system.Damping faCtors are not included in thecalculation. Output consists of criticalfrequencies in CPS and RPM for variousnumbers of blades.APPENDIX 14-2. LONGITUDINAL SHAFTINGVIBRATIONSProgram Used by J. J. McMullen Associates,Inc.Number and/or Name**~_~-121J*Category(s)Source**Machinery**Shafting and Bearing calculationsActivity**John J. McMullen Associates, Inc.**one WOrld Trade center-Suite 3047**New York, New York 10048Enqineer (s) Name-Code-PhoneProgram**EngineeringStatus**prOd*cti~nClassification**unc~a~~ifiedProgranuning LanguageComputer●*~o~TRAwDivision(Security)IvType Used**IBM 3613/40 and IBM 1~30DocumentationProgramStatus..lnforma I _ user Is GuideAbstractLumped mass system, using ,,level,,effect. Text description found in NSROCReport 3358, September 1970. Computesfrequencies up to four modes.APPENDIX 14-3. LONGITUDINAL AND TOR-SIONAL SHAFTING VIBSATIONSProgram Used by Newport News Shipbuildingand Drydock CompanyNuder and/or Name,,F-o-0~6 9.5.0251 FORCE VIBCategory (s)**Machinery**shafting and Bearing CalculationsDescriptive Program TitleSource**~ng itudinal and Tor Sional Vibrationin Propulsion Shafting SystemsActivity**Newport NeWS shipbuilding andDrydock Company**Technical systems Division**4101 Washington Avenue, NewportNews, Virginia 23607(804) 247-7500Engineer (s) Name-Code-PhoneProgrammer**A. S . Pototzky**F. E.Name-Code-PhoneSiegelK-17 +-

ProgramStatus**ActiveClassification**Unc~a S=ifiedProgrammingComputerProgramprOdUCt iOn(Security)Language**~~~~~~ ~“Typ e Used●*Honeywell 6080Availability●*Not Available for General DistributionDocumentationProgram**IncompleteAbstractStatusFORCE VIB is a computer program tocalculate the steady state longitudinalor torsional vibratory response ofbrancbed shafting systems, such as propulsionsystems. Tbe system may have amaximum of 35 elements consisting ofmasses, dampers, and springs, all withonly one degree of freedom. The massesand springs may be lumped or distributed,and the dampers nay be viscous cmsolid. The program uses the mechanicalimpedance method to calculate displacements,forces, and phase angles, whichmay all be frequently dependent. Theprogram also allow the varying of valuesto conduct parametric studies.APPENDIX 14-4. LONGITUDINAL VIBP.ATIONOF SHAFTING, 11Program Developed and Used by LittletonResearch and Engineering CorporationOutputInformation1. A plot of the blade order harmonicforce at the thIust bearing as afunction of rpm.2. A plot of the amplitudes of axialmotion at the propeller and at thethrust bearing as a function ofr~.3. Tabular data for abo”e.Inputlnforu@tion1. Shafting arrangement, diameters,and Lengths.2. Propeller mass, diameter, numberof blades, pitch, and de”elopedarea ratio (or mean “idth ratio) .3. Harmonic thrust (can be determined byprogram described in Appendix 6-2) .4. The stiffness of the thrust bearingand its foundat ion.5. Reduction gear weight.Basisfor CalculationThe propeller is represented by itsmass plus entrained water and damping,estimated by Le”is and Auslaender Vs recommendations.The shaft is represented by a distributedmass and elasticity and is assumedto ha”e a hysteretic damping (nominally4%) .The thrust bearing is representedas a concentrated mass elastically connectedto a rigid hull.This is a proprietary program notdeveloped for general distr ibntion.APPENDIX 17-1. TRAfisvERsE RE5PONSE OFA BEANProgram Used by Newport News Shipbuildingand Drydock CompanyNumber and/or Name**A-12-00 9.5.0301 Beam vibrationCategory(s)**Conceptual Design**Ship VibrationsDescriptive ProgrAm TitleSourceProgram**Vibration Analysis of BeamsActivity*.Newprt News Shipbuilding andDrydock Company*●Production computer systemsDivision**4101 Washington Avenue, NewportNews, Virginia 23607[804) 247-7500Status,*prOductiOnClassification**Unc~a~SifiedusePK091aUUfIin9Language**FOXTRANVComputer Type Used(Security)**~on~ywell 6080K-18

SpecialProgramProgramHardware*.~oneAvailability**Nok Avai~ab~e fO~ General Di~_tributionAbstractComputes the steady-state transversevibratory response of a beam withany number of intermediate flexible supports,with generalized end conditions,section properties, and loading.APPENDIX 17-2. TRANSVERSE V1BRATION OFSHAFTING AND PROPELLERProgram Developed and Used by LittletonResearch and Engineering CorporationOutputInformation1. Plots of bearing forces, in twonormal directions, as a functionof frequency.2. Plots of shaft motions, in twonormal directions, as a functionof frequency, at the propellerand at other critical locations.3. Plots of the shaft deflectioncurves at each natural frequencywithin the operating speed.The propeller is represented byits mass, its entrained water, its momentof inertia about the rotationalaxis, its moment of inertia about anaxis perpendicular to the rotationalaxis, the moment of inertia of its entrainedwater, and tbe hydrodynamic dampingin its several modes of motion.The shaft is represented as a seriesof uniform beams having distributed massand bending stiffness and hystereticdamping.The bearings are represented bytheir stiffness in translation in two directionsmutually perpendicular to theshaft axis and by their stiffness in rotationabout the same two axes. Thebearings are assumed to bend with theshaft; however, where there is flexibilitybetween shaft and bearing, e .g., rubberstaves, this flexibility, lateraland angular, is incorporated in the strutmatrix. It is generally acceptable toterminate the shaft at the after inboardlineshaft bearing.The program computes the vibrationin terms of coupled properties in thehorizontal and vertical directions. Itincludes the influence of the steadythrust (small effect) , but not that ofthe steady torque (very small) .This is a proprietary program notdeveloped for general distribution.APPENDIX 20-1. GENERAL BENDING RESPONSEPROGRANProgram Developed and Used by Naval shipResearch and Development CenteX4. Plots of the steady plus harmonicbending moments in the shaft ofthe aftemnost bearing.e**GBRp5. Computer tables for above.InputInformation1. Shafting arrangement, diameters,and lengths.2. Propeller weight and moment of inertiaabout its rotation axis, diameter,number of blades, pitch,and developed area ratio.3. Stiffness or flexibility matricesfor each bearing about axes perpendicularto the axis of rotation(force and rotation ).4. Horizontal and vertical harmonicforces and moments, and the steadythrust (can be determined by theprogram described in Appendix 6-2) .Basisfor CalculationsCategory (s)**L~t~ra~ , Longitudinal, and TorsionalBeam ~ibrations**Bending coupled with TorsionalBeam Vibrations**Whirling Vibrations of PrOPellerShaftsDescriptive Program TitleBource**GeneraL Bending ~~sponse programActivity*.NavaI Ship R~~~~r~h ~~d DevelopmentCenter**Bethesda, Maryland 200S4Engineer (s)Program**f.fi~hae~ E. Golden●*Franci~ M. HendersonStatus* ,Active prOdUct iOnK-19

Classification**unc~a~~ifiedProgrammingComputerOutputSpecialProgram(Security)Language*.p~~~~ ~“**CDCTyp e UsedPlotting~~~~ SerieS..~~ ~~~~ p~o~~Software/OperatiOn**overlays for Program Subroutines.*Open Core tO optimize stora9eAvailability**Availability for General Distributionthrough Da”id Taylor NavalShip Research and DevelopmentCenterDocumentationProgram**CompleteAbstractThe General Bending Response Program(GBRP) consists of the union ofthree programs: General Bending Res~nseCOde 1 (GBRC1) for lateral,longitudinal, and torsional vibrations;GBRC2 for vibrations involving bendingcoupled with torsion; and GBRC3 forwhirling vibrations of propeller shafts.The latter two codes resulted from anextended application of the mathematicalmodel used in the first code. Theprogram formulates the finite differenceequations which approximate the boundary-valueproblem representing thesteady-state motion of a vibrating nonuniformmass-spring system such as aship hull or shafting in bending. Theprogram calculates natural frequenciesand mode shapes and the response tospecified harmonic driving forces andmoments. The program can represent aship hull connected elastically to othersystems such as the propulsion systemand to sprung masses. Longitudinal ortorsional vibration problems can alsobe solved by dividing each beam intosections connected by springs, thus reducingthe model to a mass-spring system.See Reference (27) .APPENDIX 20-2. SHIP HULL VIBRATORYRESPONSEProgram Used by USS Engineers and consultants,Inc.Number and/or Name**A-~2-~~~Category (s)s~~”~**Conceptual Design**Ship VibrationsDescriptive Program TitleSource**Siin”lated Ship-HullActivityvibrationn.USS Engineers and consultants,lnc .**fjo~Gr~~t st~e~t**Pittsburgh, Pennsylvania 15230Engineer (s) Name-Code-PhoneProgramClassification**F. Ronald Griffith(412) 433-6517Status**prOd~ction**rJnC~aSSifiedPrograming**FoR~~~(Security)LanguageIvComputer Type usedSpecialSpecial**I-DC 6500**N~ne**NoneHardwareSoftware/OperationProgram Size-Source Deck cards**4,000 cardsProyran Size-Object Core Words*,I~oK oct=l WOrdSAverage Running Time (Min)Programcost —**3 Mi*”te~Availability**Time Sharing ServiceCall F. R. Griffith**NegotiableK-2o

———Documentation Status**Informal completeProgramAbstractThe purpose of SHRVS is the accurateprediction of the vibratory I-esponseof a ship hull to either steady-State or transient loads applied in thevertical centerline plane of the hull.Factors considered include cargo distribution,bulkhead location, machineryspace location, as well as the flexuraland shear stiffness of the main-hullgirder and of the double-bottom structure.See Reference (32).K-21

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