% 无阻尼二自由系统固有频率的程序 20180401A
w) ~8 j: z w/ j2 O5 Lm1=100;m2=100;k1=200;k2=400;% 2 w5 n1 _$ m5 v! T5 ?5 M
c1=0;c2=0;
# n4 g# r: G9 ]% ex0=[1;0];xd0=[0;0];tf=50;dt=0.1;
7 T( x, ~+ _( G$ E4 t$ h( rM=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];! |) L3 V. R% B% f8 S. ?
c=[c1+c2,-c2;-c2,c2];
, K4 \$ u0 v* F. n# t6 RA=[zeros(2,2),eye(2);-M\k,-M\c];2 R4 T8 W$ C- \7 t& l
y0=[x0;xd0];
; y* z9 y$ o3 i6 ^- F3 Ufor i=1:round(tf/dt)+1
8 _6 b5 w6 a1 C8 H9 e; S$ N" }' X5 N t(i)=dt*(i-1)+ A Z' Q! n) \
y(:,i)=expm(A*t(i))*y0;1 R0 B3 Z/ C: c( m! k, v
end0 {; Q! P6 D! Q5 d5 q" |7 F/ D
subplot(2,1,1),plot(t,y(1, ),grid
3 E6 `+ F0 H' C4 l& [subplot(2,1,2),plot(t,y(2,),grid
2 t& Y. N- I' p. x1 C* m0 d4 o[p,lamda]=eig(A)
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lamda =
m% C5 z3 v! ~) u7 r Columns 1 through 2) Y+ o7 f, U# t6 @. y. w
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
4 ^, @( p) X% ]: d( h& E 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
7 ]& q& b7 H3 ]& C: ^0 m. j 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i I- A6 ?* q5 y5 F7 R& e
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
8 @% \- y" {& |) b Columns 3 through 4
* |0 O3 t' t- D3 P8 | 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
$ s+ r5 a% i8 Z) u5 b+ _' U 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i7 f, Q% U o. Z( c" B" X! Y
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
2 M! m2 t+ M$ U" i K" U# g 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i$ `1 o3 w7 Q2 f: d8 ?* m/ l, f" |: o
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发表于 2018-4-16 19:41:12
