日期:23-03-13 時(shí)間:12:14 來(lái)源: 益榮金屬
將(3-21)帶入上式,得:
1/2mv1R2(L-2/3R)=m[3R2v1/(ξ1+R)2]·[1/6(L-ξ1-R)(ξ1+R)2+1/3(ξ1+R)2-1/4(ξ1+R)3]
+(M0U+M0C)t+N0?0w(t)dt
整理上式,得:
1/2mv1R2(L-2/3R)=3mR2v1[1/6(L-ξ1-R)+1/3-1/4(ξ1+R)]
+(M0U+M0C)t+?0N0w(t)dt
=3mR2v1[1/6L+1/3-5/12(ξ1+R)]+(M0U+M0C)t+N0?0w(t)dt (3-24)
式(3-24)兩邊分別對(duì)時(shí)間t求導(dǎo),得:
0=-5/4mR2v1ξ1+M0U+M0C+N0w(t) (3-25)
式(3-25)兩邊再分別對(duì)時(shí)間1求導(dǎo),得:
5/4mR2v1?1=N0Ψ
將(3-21)式Ψ=3R2v1/(R+ξ1)2代入上式,得:
5/4mR2v1?1=N0[3R2v1/(R+ξ1)2]
即5/12m(R+ξ1)2?1=N0 (3-26)
方程(3-26)的初始條件為:
ξ1(T1)=(√1+R2-1 (3-27)
且:
é1(T1)=4(M0U+M0C+N0w1)/5mR2v1 (3-28)
將ξ2=R代入式(3-13))即可獲得(3-27)式:將t=T1,w(T1)=w1帶入(3-25)式,可得(3-28)式。
在t=T2(即絞線CD移動(dòng)到固支邊)時(shí)第二相結(jié)束,此時(shí)ξ1=L-R。鉸線的移動(dòng)規(guī)律由(3-26)式描述,T2也由該式獲得。
撓度w2可計(jì)算為
w2=?T1T2Ψ(t)dt=?T1T2 [3R2v1/(R+ξ1)2]dt (3-29)
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