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Section18 NormalModesofPreloadedStructures Section18NormalModesofPreloadedStructures NORMALMODESWITHDIFFERENTIALSTIFFNESS 18 3PROBLEM 14 NORMALMODESWITHPRELOAD 18 7PROBLEM 14 MODESOFPRELOADEDSTRUCTURE 18 9INPUTFILEFORPROBLEM 14A MODESWITHOUTPRELOAD 18 10PARTIALOUTPUTFILEFORPROBLEM 14A MODESWITHOUTPRELOAD 18 11INPUTFILEFORPROBLEM 14B MODESWITHPRELOADUSINGSOL106 18 12PARTIALOUTPUTFILEFORPROBLEM14B MODESWITHPRELOADUSINGSOL106 18 13INPUTFILEFORPROBLEM 14C MODESWITHPRELOADUSINGSOL103 18 14PARTIALOUTPUTFILEFORPROBLEM 14CMODESWITHPRELOADUSINGSOL103 18 15 NormalModesWithDifferentialStiffness Calculatethemodesofstructureswithpreloads largechangesingeometry and ornonlinearmaterials NormalModesWithDifferentialStiffness Cont LargeGeometryChanges u 1 NonlinearMaterial k 1 F k 0 K0 k1 NormalModesWithDifferentialStiffness Cont Proceduresforobtainingfrequenciesofapreloadedstructure Method1UseSOL106 Includelinearornonlinearmaterialpropertiesasrequiredbymodeling Ifmaterialislinear thenonlylinearmaterialpropertiesarereferenced IncludePARAM LGDISP 1intheBulkDataSection Onlytheresidualstructure SEID 0 maycontainnonlinearelements Allupstreamsuperelementsmustbelinear AMethod XCaseControlCommandabovethefirstsubcasecallsouttheappropriateEIGRLentry IncludePARAM NMLOOP XwhereX0 ThenonlinearnormalmodeswillbecomputedatthelastiterationloopofeachsubcaseinwhichaMethodcommandappears NormalModesWithDifferentialStiffness Cont Proceduresforobtainingfrequenciesofapreloadedstructure Method2UseSOL103 Materialmustbelinear Twosubcasesarerequired Thefirstsubcaseisastaticsubcasecallingoutthepreload Thesecondsubcasecalculatedthemodeswithamethod xcallout Thesecondsubcasemustalsocontainastatsub ycommand wherey subcaseIDofthefirstsubcase Problem 14 NormalModesWithPreload Problem 14 ModesofPreloadedStructure Considerthesimplysupportedbeamasshownbelow Calculatethefirstbendingfrequency WithoutpreloadWithpreloadusingSOL106WithpreloadusingSOL103 Problem 14 ModesofPreloadedStructure Cont SolutionFileForProblem 14A ModesWithoutPreload SOL103TIME600CENDTITLE NormalModesExampleSUBCASE1METHOD 1SPC 1VECTOR ALLBEGINBULKPARAMWTMASS 00259PARAMCOUPMASS1EIGRL130PBARL11I A A2 1 1 1 1 1CBAR11120 1 0 CBAR21230 1 0 CBAR31340 1 0 CBAR41450 1 0 CBAR51560 1 0 CBAR61670 1 0 CBAR71780 1 0 CBAR81890 1 0 CBAR919100 1 0 CBAR10110110 1 0 MAT111 7 3 101GRID10 0 0 345GRID210 0 0 345GRID320 0 0 345GRID430 0 0 345GRID539 99990 0 345GRID649 99990 0 345GRID760 0 0 345GRID870 0 0 345GRID980 0 0 345GRID1090 0 0 345GRID11100 0 0 345SPC1112341SPC1123411ENDDATA PartialOutputFileForProblem 14AModesWithoutPreload 0EIGENVALUEANALYSISSUMMARY READMODULE BLOCKSIZEUSED 7NUMBEROFDECOMPOSITIONS 2NUMBEROFROOTSFOUND 3NUMBEROFSOLVESREQUIRED 41NORMALMODESEXAMPLEAPRIL8 1998MSC Nastran4 6 98PAGE50SUBCASE1REALEIGENVALUESMODEEXTRACTIONEIGENVALUERADIANSCYCLESGENERALIZEDGENERALIZEDNO ORDERMASSSTIFFNESS112 239398E 041 496462E 022 381693E 011 000000E 002 239398E 04223 549898E 055 958102E 029 482614E 011 000000E 003 549898E 05331 771818E 061 331096E 032 118506E 021 000000E 001 771818E 06 SolutionFileForProblem 14B ModesWithPreloadUsingSOL106 SOL106TIME600CEND TITLE NormalModeswithDifferentialStiffnessMETHOD 10SUBCASE1NLPARM 1SPC 1LOAD 1DISPLACEMENT ALL BEGINBULKPARAMCOUPMASS1PARAMWTMASS 00259PARAMLGDISP1NLPARM15AUTO525PWNO A A 0011 7PARAM NMLOOP 5 EIGRL 10 3PBARL11I B B2 1 1 1 1 1CBAR11120 1 0 CBAR21230 1 0 CBAR31340 1 0 CBAR41450 1 0 CBAR51560 1 0 CBAR61670 1 0 CBAR71780 1 0 CBAR81890 1 0 CBAR919100 1 0 CBAR10110110 1 0 MAT111 7 3 101GRID10 0 0 345GRID210 0 0 345GRID320 0 0 345GRID430 0 0 345GRID539 99990 0 345GRID649 99990 0 345GRID760 0 0 345GRID870 0 0 345GRID980 0 0 345GRID1090 0 0 345GRID11100 0 0 345LOAD21 1 1SPC1112341SPC1123411FORCE1110500 1 0 0 ENDDATA PartialOutputFileForProblem 14BModesWithPreloadUsingSOL106 REALEIGENVALUESMODEEXTRACTIONEIGENVALUERADIANSCYCLESGENERALIZEDGENERALIZEDNO ORDERMASSSTIFFNESS112 735837E 041 654037E 022 632481E 011 000000E 002 735837E 04223 748482E 056 122484E 029 744236E 011 000000E 003 748482E 05331 816508E 061 347779E 032 145057E 021 000000E 001 816508E 06 SolutionFileForProblem 14C ModesWithPreloadUsingSOL103 SOL103DIAG8CEND TITLE NormalModeswithDifferentialStiffness SPC 1DISPLACEMENT ALL SUBCASE1LOAD 2 SUBCASE2METHOD 10STATSUB 1 BEGINBULKPARAMCOUPMASS1PARAMWTMASS 00259 EIGRL 10 3PBARL11I B B2 1 1 1 1 1CBAR11120 1 0 CBAR21230 1 0 CBAR31340 1 0 CBAR41450 1 0 CBAR51560 1 0 CBAR61670 1 0 CBAR71780 1 0 CBAR81890 1 0 CBAR919100 1 0 CBAR10110110 1 0 MAT111 7 3 101GRID10 0 0 345GRID210 0 0 345GRID320 0 0 345GRID430 0 0 345GRID539 99990 0 345GRID649 99990 0 345GRID760 0 0 345GRID870 0 0 345GRID980 0 0 345GRID1090 0 0 345GRID11100 0 0 345LOAD21 1 1SPC1112341SPC1123411FORCE1110500 1 0 0 ENDDATA PartialOutputFileForProblem 14CModesWithPreloadUsingSOL103 1NORMALMODESWITHDIFFERENTIALSTIFFNESSAPRIL9 1998MSC Nastran4 6 98PAGE90SUBCASE2REALEIGENVALUESMODEEXTRACTIONEIGENV
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