理论力学综合教程-振动课件.ppt

1、)sin(0eqeqtFkm 0 kyym kWkWstst/kxxkWFWdtxdmst)(220kxxm 0kxxm 022xxmknn 积积分分常常数数2121,sincosCCtCtCxnn212221/tan,CCCCA:令令)sin(tAxn fTTnn2122周周期期0eqeqqkqm 0kxxm 加加的的力力或或力力矩矩。需需要要在在这这一一坐坐标标方方向向施施移移，义义坐坐标标方方向向产产生生单单位位位位等等效效刚刚度度：使使系系统统在在广广eqk向向施施加加的的力力或或力力矩矩。度度，需需要要在在这这一一坐坐标标方方速速义义坐坐标标方方向向产产生生单单位位加加等等效效质质量

2、量：使使系系统统在在广广eqm0eqeqqkqm 02qqn tCtCqnncoscos21tAqnsin初初始始速速度度。初初始始广广义义坐坐标标；振振动动的的初初位位相相；振振动动的的振振幅幅；系系统统的的固固有有频频率率；0000n2020eqeqarctanqqqqqqAmknnN/m1031226.lEAk0 kxxm 1ns63.19)sin(mktAxnvvxx(0)(0),0)0(m0127.00nvAtxsin19.630127.0tmAWFtmAxmFWnnTnnTsinsin22 kN2.88)(22maxnnTAgmmAWFtxsin19.630127.0EImglEI

3、Wly3333stFmgym EIFlEIlFyy3333st等效刚度等效刚度klEIkyykF3st3Fmgym styykF0 kyym EImglEIWly3333st)sin(tAyn33lEIk 21eq111kkkeqststststststkmgkkmgkmgkmg)11(21212211)(2121kkmkkmkeqn21eqkkkststkFkF2211,steqstkkkFFmg)(2121mkkmkeqn21143433471kkkkkk1342234149kkkk143433471kkkkkk1342234149kkkk123411423kkkkeqmkmkeqn142

4、31coscos22FamgldtdJO)sin(akFstsin,1cos则则考考虑虑到到微微转转角角,akmglstcoscos22FamgldtdJO)sin(akFstsin,1cos则则考考虑虑到到微微转转角角,akmglst222)(kaaakmgldtdJstO02kaJO mklaJkaOn)sin(tAxn)cos(tAxvnn)(cos21212222tAmmvTnnmgxxkVstst)(2122)(sin2121222tkAkxVnmgkst22max21AmTn2max21kAVmaxmaxVTmkn)(cos21212222tAmmvTnn)(sin2121222t

5、kAkxVn)sin(tAn2222maxmax21)(21nAmllmT222maxmax21)(21AkaakVmaxmaxVTmklanRCORCO222121CCCJmvTcos)(rRmgVrrRrvrRvCCC)()(22)(43rRmTcos)()(4322rRmgrRmVTLRCOcos)()(4322rRmgrRmVTLsin)(rRmgL2)(23rRmL 2)(23)(ddrRmLt0)(ddLLt0sin)(23grR 0)(32rRg RCO0)(ddLLt0sin)(23grR 0)(32rRg)(32rRgnRCO)sin(tAn2sin)(2)cos1)(2rR

6、mgrRmgV2222max2max)(43)(43nArRmrRmTsin有有考考虑虑到到微微振振动动时时,2)(21rRmgV2max)(21ArRmgVRCO2222max2max)(43)(43nArRmrRmT2max)(21ArRmgVmaxmaxVT)(32rRgnvFccdtdxckxdtxdm2202222xdtdxndtxdn粘粘性性阻阻尼尼力力弹弹性性恢恢复复力力xcFkxFckmcnmkn2,2:令令02222xdtdxndtxdn0222nnrr222221nnnnrnnrrtex trtreCeCx2121222221iinnrnnrnn)sin(22tnAexnn

7、tmkc20(0)(0),0)0(vvxx0022n022n20020tan)(nxvnxnnxvxA22)sin(ntAexnddnt:其其中中tAxntdsinentAentAeTdA2A12222nTnddmkcnn2222222111122nddnndffTnT)ee(222221tntnntnnCCex222,1nnnrnrr21)(21tCCexnt11km0e激激振振力力的的初初相相位位激激振振力力的的圆圆频频率率力力幅幅简简谐谐激激振振力力HtHF)sin()sin(22tHkxdtxdm)sin(222thxdtxdnmHhmkn2:令令)sin(222thxdtxdn.;2

8、121特特解解通通解解xxxxx)sin(1tAxn)sin(2tbx)sin()sin()sin(22thtbtbn22nhb)sin()sin(22thtAxnn22nhbkHhbn200(1 1)若若.,bbn nn n单单调调上上升升频频率率随随着着振振幅幅0 0(2 2)若若.0,bb增增大大而而减减小小随随着着频频率率振振幅幅(3 3)若若n n幅频特性曲线幅频特性曲线)sin(2tBtxnnhB2)sin(22tthxnnthbn2简简谐谐激激振振力力tHFsintHdtdxckxdtxdmsin22thxdtdxndtxdnsin2222mHhmcnmkn,2,2:令令)()(

9、21txtxx：分分方方程程的的解解有有阻阻尼尼自自由由振振动动运运动动微微)(1txtnAxnnt221sine设设其其为为运运动动微微分分方方程程的的特特解解,)(2tx)sin(2tbx22222222tan4)(nnnnhb)sin()sin(e22ntbtnAxnt振振幅幅比比阻阻尼尼比比频频率率比比0 0bbnnn22222012tan4)1(1bb曲曲线线族族幅幅频频特特性性曲曲线线曲曲线线族族相相频频特特性性曲曲线线曲曲线线族族幅幅频频特特性性曲曲线线曲曲线线族族相相频频特特性性曲曲线线曲曲线线族族幅幅频频特特性性曲曲线线曲曲线线族族相相频频特特性性曲曲线线 kcmkcmFex

10、rOxeO1kcmFexrOxeO1errrFkxxcxm tamkxxcxmsin2rrr tBxsinr2222212arctan,21 aB0eexxkxxcxm tactkakxxcxmcossin tactkakxxcxmcossin 2211cossintBtBx2222012arctan,211eqkFB21222112arctan,211 aB22222212arctan,212 aB21222112arctan,211 aBtBtBtBxsincossin22112232222212arctan,2121 aB22222212arctan212,aB21222112arcta

11、n211,aBtBtBtBxsincossin22112232222212arctan2121,aB2232222212arctan,2121 aB220222200ccdcosddBcttBctxctxFWTTtFtFtFtFsincoscossinsinsin0000sindcossin000BFtxtBFTtxtFWTdcossin00Fsindcossin000BFtxtBFTtxtFWTdcossin00FBcFsin0c20FsinWBcBFW2eq2eq2121qkVqmT,VTLqLqLt，0dd2eq2eq2121qkVqmT,2eq2121qcqqqqciiiirrVTLqqLqLt，ddOOLJ 2eq2eq2121qkVqmT,EVT0eqeqqqkqqm