Treść książki
Przejdź do opcji czytnikaPrzejdź do nawigacjiPrzejdź do informacjiPrzejdź do stopki
firstnaturalfrequenciesandbucklingcriticalforces
DynamicalstabilityofVariablecrosssectionbars-
CHApTER2
2i1iIntroduction
Arational
useofmaterialswhatisconnectedto
constructionwhichwillensurethatthe
acapabilityofcalculationofbarswith
problemsofbendingistabilityandVibrationsofframesmadeofVariablecrosssection
arebeingsolVedwith
criticalbucklingforcesȂbothseparat
bedeterminedfromth
bymeansofthe
beamswaspresentedbyConwayandDubil(1965)iEceetali(2007)assumedaneXponential
Variabilityofbeamwidthwhat
wayiusingthe
Lauraetali(1996)comparedValuesofthe
meansofthree
the
onesiThemulti-segment(stair-shaped)beamswereanalyzedalsobyNaguleswaran(2002i
2004)iMao(2011)comparedthe
(2002)tohisownresultsobtainedbyuseoftheAdomiandecompositionmethodfortwo-step
beamwithconstantthi
constantwidthandVaryingheightȂreachingthe
(2013)determinednaturalVibrationsformultiple-steppedbeamsusingthe
singularconVolutioniVazandLimaJunior(2016)determinednumericallythe
differentialquadraturetechniqueȂreachingVerygoodconformitybetweenthetwofirst
Thereisalotofitemsinthe
designandshapingofengineeringconstructionsrequ
methodsitheopt
methodofseparat
Besselfunctionsofthesecon
manymethodsi
eEuler-BernoullidifferentialequationofbeamdeflectioniItssolutio
cknessandstep-Varyingwidthaswellasforthreestepbeamswith
enabledtosolV
imizedRayleigh-Ritzmethodithe
literatureconcerningcalculationofnaturalfrequenciesand
ionofVariablesiForbeamsofbilinearlyVaryingthickness
dimensionlessfrequencyfromthepaperbyNaguleswaran
elyandtogetheriTheVibrationformandfrequencycan
crosssectionVary
aneedofsuchdimensioningofeachelementofthe
elementismatchedto
dimensionlessfundamentalfrequencyobtained
dkindfortruncat
ethe
DzeXcellentdzconformityiDuanandWang
equationofbeamVibrationsinaneXact
ingalongthe
edconeandtruncatedwedge
iresiamongothers
finiteelementapproachand
itsloadiItforcesiinturni
barlongitudinalaXisi
modifieddiscrete
iaproper
natural
bars
by
n
i
Vibrationformofbeamswithmultiplestepchangesincrosssectionandcompareditto
eXperimentalresultsiTanetali(2016)alsoconsiderednatural(transVersal)Vibrationsof
13
