% 无阻尼二自由系统固有频率的程序 20180401A# a* ^" ?5 z# n& r+ d/ S
m1=100;m2=100;k1=200;k2=400;%
/ l- m0 g3 g- w5 s+ cc1=0;c2=0;
" \! l' @* _9 `3 }9 P/ O2 ~x0=[1;0];xd0=[0;0];tf=50;dt=0.1;4 h7 F2 F; M" ^* |# {1 D
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
6 r) S4 x/ W; O0 K* V- vc=[c1+c2,-c2;-c2,c2];) y( M' g0 @' }6 b9 K* N% A5 k8 h
A=[zeros(2,2),eye(2);-M\k,-M\c];4 } l; T7 ~! z9 _! h
y0=[x0;xd0];
7 O; \& u5 l! A0 a# Dfor i=1:round(tf/dt)+12 ?" p4 R$ v! V, @7 u! H
t(i)=dt*(i-1)
" ]6 q; I% U7 c9 g) u- r4 B: }0 O y(:,i)=expm(A*t(i))*y0;; e# i9 k8 C/ H+ ], i |; p
end
3 V" a% c& R( ?8 Jsubplot(2,1,1),plot(t,y(1, ),grid
6 N' y! C! ~ H' ?( K& O1 e5 F- o( Usubplot(2,1,2),plot(t,y(2,),grid+ V& `6 E3 x+ G! u
[p,lamda]=eig(A)" s4 p/ b( I c$ I2 q: @
1 ?$ @4 a" u' a( Y$ t
( p! h; e! A1 t! `% n7 j. }
+ s2 ^- }/ {- V, a! p
- P, V, f: i3 j( w2 J# Tlamda =
9 f0 @- _5 `7 [5 [ Columns 1 through 2
; y" a u9 R4 n6 S4 @% s 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i" l: @0 d/ y% ~# g
0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
9 J/ M& y2 `4 l& J 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i& e6 E: q) w v0 v
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i9 ~% |9 a( V3 ~ `; W6 L. k
Columns 3 through 4* R T3 f% [" j
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i( \( ?, h5 {: R# j1 W
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
" u7 ~' T2 K7 K$ J2 T2 v* Q -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i( A( w2 z. d& Z* ]: H
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i6 z$ ]) z2 U( d
; q* w1 f6 A5 F( E9 X# r/ ?! V9 r3 P
2 O0 y5 c& }) ~ |* T2 v' \4 c) N
1 r9 u# H. f9 @3 ^ |
发表于 2018-4-16 19:41:12
