土動(dòng)力學(xué)試題

QUESTIONSFindthenaturalfrequencyofvibrationofafoundationwithamassmsupportedbyasoilthathasexperiencedastaticdeflectionof0.5inchesunderthatmass.Findtheperiodofoscillationandthenaturalfrequencyofvibrationofafoundationwithaweightof60kNandasoil(spring)constantof103kN/m.Determinethemaximumandminimumforcesplacedbyavibratingmachine’sfoundationuponitssoilsub-grade,if:(1)themachineanditsfoundationweigh40kN,(2)thesoil’sequivalentspringconstantis400kN/cmand(3)themachineoperatesat800rpm.AssumethattheforceQo(kN)uponthefoundationis8sin31.Determine(1)whetherafoundation-soilsystemisover-damped,criticallydampedorunder-damped,(2)thelogarithmicdecrement8,and(3)theratiooftwosuccessiveamplitudes,iftheweightofthefoundationis60kN,thesoilspringconstantis11MNpermeterandthedampingcoefficientis200kN-s/m.Determine(1)theundampednaturalfrequencyfnofthefoundation,(2)theamplitudeofthemotion,and(3)themaximumdynamicforcetransmittedtothesub-grade,foranelectricalgeneratordrivenbyadieselengineplacedonaisolatedfootingthatweighs140kN.Thespringconstantandthedampingratioofthesoilis12x104kN/mand0.2respectively.ThevibratingforceQis46kNat3=157rad/s.Calculatethenaturalfrequenciesofthesystem3n1and32shownbelow,ifW1=25lbandW2=5lb,andthespringconstantsarek1=100lb/inandk2=50lb/in.CalculatetheamplitudesofvibrationZ1andZ2forthetwomassesofExample1,ifavibratoryforceQ=10sin3t(lb)isappliedtothemassmlwithafrequency3=78.54radians/s.Determinethenaturalfrequencyoftheundampedfreevibrationofthesystemshownbelow.Determinethenaturalfrequencyoftheundampedfreevibrationofthe

systemshownbelow.Determinethenaturalfrequencyandtheperiodofthesystemshownbelow.Forasingle-degreeoffreedomsystem,thenaturalperiodTis,Theinverseofthenaturalfrequency,Equivalenttothelinearnaturalfrequency,ExpressedinHertz(Hz).Whatisthespectralaccelerationofasingle-degree-of-freedomsystem?Itistheminimumaccelerationexperiencedbythesysteminresponsetoaperturbation.Itistheaverageaccelerationexperiencedbythesysteminresponsetoaperturbation.Itisthemaximumaccelerationexperiencedbythesysteminresponsetoaperturbation.Itistheabsoluteaccelerationexperiencedbythesysteminresponsetoaperturbation.Forthefollowingharmonicoscillator,howisthestiffnessbestdescribed?Thestiffnessisbestdescribedastheforceactingontheideallinearspring.Thestiffnessisbestdescribedastheforcedeflectingthespringadistanceof1unit.Thestiffnessisbestdescribedasthemagnitudeofthespringdeflection.Thestiffnessisbestdescribedasthereciprocalofdeflection.Whendoesthenaturalperiodofabuildingcoincidewithanearthquake’speriod?Theycoincidewhenthenaturalfrequencyisatitsmaximum.Theycoincidewhentheaccelerationisatitsmaximum.Theycoincidewhenthedisplacementisatitsmaximum.Alltheaboveareright.Theperiodofastructureiscorrelatedwiththe,I.Themassofthestructure,II.Thestiffnessofthestructure.Ionly.IIonly.IandII.Noneoftheabove.ConsiderthenaturalperiodTandtheaccelerationaofasingle-degree-of-freedomsystem.Whenthemassmofthesystemincreases,howareTandaaffected?Tincreasesandaincreases.Tincreasesandadecreases.Tdecreasesandaincreases.Tdecreasesandadecreases.Ifkisthestiffnessand;Aisthedeflectionofasystem,whichofthefollowingrelationshipsdescribebesttherigidityR?TOC\o"1-5"\h\z1/kk;A;1/AAmassmhangsfromtwo“ideal”springs;whatisthetotalcompositespringconstantforthesystem?k1+k2k1k2

1/k1+1/k2(k1k2)/(kl+k2)19有一彈性自由桿，長(zhǎng)L=20m,應(yīng)力波速C=4000m/s,當(dāng)一端受瞬態(tài)激勵(lì)后，實(shí)測(cè)速度波形如下圖，推算彈性桿(忽略材料的阻尼影響)另一端在3.5ms、5.5ms和7.5ms時(shí)的質(zhì)點(diǎn)速度。Vm/s2"1234；678?t(ms)20從運(yùn)動(dòng)方程8bd2u*Fi式中u,為彈性體位移張量，。”為彈性體應(yīng)力張量，'為彈性體坐標(biāo)張量，試推出以位移表述的三維彈性體彈性波傳播的完備數(shù)學(xué)描述。21假設(shè)總應(yīng)力不變化，從有效應(yīng)力觀點(diǎn)，利用Coulmb準(zhǔn)則