第二讲(单自由度系统自由振动)

2009226200918123121234512Fourier1Duhamel2Fourier3Laplas12311)()()()(tFtkxtxctxm=++&&&FNmx−=&&(,)Nfxx=&Nkxcx≈+&(0,0)(0,0),ffkcxx∂∂==∂∂&(0,0)(0,0)(0,0)ffNfxxxx∂∂≈++∂∂&&232-12.10222120badmlxcxkkxlll⎛⎞+++=⎜⎟⎝⎠&&&2-2rmgR2.11203()gRrθθ+=−&&3DEAkl=12111kkk=++L313BEIkl=2pCGIkl=2112kkk=++L22-42eqJml=2teqkkamgl=−2eqJmL=2teqkkamgL=+2-32221RmrmJmeq++=242231)()(Rkkrkkkeq+++=Jmeq=2421413232lGdlGdkeqππ+=2-52-62-72.42-82.53eLmmρ=+22213vsAJmbmbma++=2-92.32.62121eekikJiJ==32222200cos()TccWFxdtcAtdtcAπωωωϕπω==+=∫∫&4eqmgcAµπω=83eqAcγωπ=eqacπω=4)()()()(tFtkxtxctxm=++&&&2,2,2nnnckcccmmmcωζωζω====)(1)()(2)(2tFmtxtxtxnn=++ωζω&&&30)(=tF10)()(2)(2=++txtxtxnnωζω&&&)(1)()(2)(2tFmtxtxtxnn=++ωζω&&&0)(≠tF2121022=+nsω0)()(2=+txtxnω&&nisω±=2,112nnititxceceωω−=+10)()(2)(2=++txtxtxnnωζω&&&cossinnnatbtωω=+sin()nAtωϕ=+22arctanaAabbϕ=+=nxbxaω/,00&==2200020arctannnxxAxxωϕω=+=&&200)0(,)0(xxxx&&==ab2200020sin()sin(arctan)nnnnxxxAtxtxωωϕωω=+=++&&0022020arctanxxmkxxAnnn&&ωϕωω==+=titiitinnneAeAeAeZωωϕϕω=⋅==+)(2-102.1232313cos()3mglEIxtEIml=30oJmgaϑϑ+≈&&2-112.13sin0oJmgaϑϑ+=&&224oTJmgaπ=[][]2211111222222222()()4()()4sccscsccscTJJmHhmgamgHhTJJmHhmgamgHhππ⎧++−=+−⎪⎪⎨⎪++−=+−⎪⎩2oCJJma=+2-12·441212121212,,3232ppppGIGIddkkIIllππ====2-132112222122nADrkkrrJJrω+=[phone]()()0ADAArrJJkkrrθθ+++=&&210)()(2)(2=++txtxtxnnωζω&&&0222=++nnssωζω122,1−±−=ζωζωnns)(1211212221ttttstsnnnececeececx−−−−+=+=ζωζωζωconsteesststs≠≠122121ss≠1ζ)(1211212221ttttstsnnnececeececx−−−−+=+=ζωζωζωtstnetccetccxζω−+=+=)()(21211=ζ21ss=2212111212()nnnitittststxceceececeωζωζζω−−−−=+=+22,11ζωζω−±−=nnis1ζ12(cossin)ntddeCtCtζωωω−=+12(cossin)ntddxeCtCtζωωω−=+sin()ntdAetζωωϕ−=+221122arctanCACCCϕ=+=21dnωωζ=−00102ndxxCxCζωω+==&220000200()arctannddnxxxAxxxζωωϕωζω+=+=+&&122,1−±−=ζωζωnnsNyquistnζω232221ddnTππωωζ==−21221δζππδ=≈⎛⎞+⎜⎟⎝⎠111111lnlnndjjAxTjAjxδζω++===2221πζδπζζ=≈−()1nindnidtTitTiAAeeAAeζωζωζωη−−++===1lnlnindiATAδηζω+===2-1420kg0.01mkcln2=0.6931msNcmNk/.1063.4/1022.225×=×=2-15mx025.0)0(=smx/3.0)0(−=&0.5s2-1612.5Ns/m