% 无阻尼二自由系统固有频率的程序 20180401A W: i! P( x. z. m+ y3 K, o. q( [
m1=100;m2=100;k1=200;k2=400;% ! E6 `& m$ ^" q& s. p& ^8 l
c1=0;c2=0;, C+ h3 ^1 U# o& l% v+ K8 h; o
x0=[1;0];xd0=[0;0];tf=50;dt=0.1;. X0 a6 C ^% ^: \8 G4 K7 m
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];, D1 d3 H* b! I$ o. D! q" |
c=[c1+c2,-c2;-c2,c2];7 ~. `! V$ a& o; |+ g
A=[zeros(2,2),eye(2);-M\k,-M\c];
6 s6 f, z! f+ {: Oy0=[x0;xd0];8 i: D \/ H3 Z2 W0 W
for i=1:round(tf/dt)+17 v& |" y# o8 ?( s$ `% w
t(i)=dt*(i-1)
( |; w3 c0 {6 h6 i" P y(:,i)=expm(A*t(i))*y0;7 T0 x; {% g5 _3 F0 h7 y
end0 I8 y+ r) R F) r: ~( t* O
subplot(2,1,1),plot(t,y(1, ),grid
1 ^/ C: w, |7 osubplot(2,1,2),plot(t,y(2,),grid
0 ?, M9 N9 y- Z4 _0 r( F[p,lamda]=eig(A)3 t: ?# C' r' T$ }
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. |* @# S9 d( Z) Alamda =
; J: e2 n; C2 e! J4 s7 M- O Columns 1 through 20 I0 z; L/ v3 B) D3 c( l/ a' b
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i# q- S+ D2 ^5 }2 k; k
0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
2 }; d4 r" Z( n. |, M 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i4 `4 A+ P+ G9 \5 g8 Y3 i
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
0 i$ H$ G0 e! l) ` Columns 3 through 4
) b* l6 H2 v3 U* Q8 Q B" p 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i3 d" ~% E( @0 V0 ^, S3 y
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
6 a! d$ n4 [. j -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i7 K: I6 ~# m7 v2 ^( X
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
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发表于 2018-4-16 19:41:12
