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% 無阻尼二自由系統(tǒng)固有頻率的程序 20180401A( Q7 z1 O; D" Q& ^* m
m1=100;m2=100;k1=200;k2=400;% 4 y9 E) H1 M2 F; Y
c1=0;c2=0;
" k v9 c, @9 Nx0=[1;0];xd0=[0;0];tf=50;dt=0.1;- u/ G$ \5 Z O" t$ S
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];
- R% j- n/ i- f- P6 q) O' k( ac=[c1+c2,-c2;-c2,c2];: U( k. V8 V' k% v1 i* P8 G
A=[zeros(2,2),eye(2);-M\k,-M\c];
7 A! @, K* ^" U& t% ^+ Z6 gy0=[x0;xd0];
" _ I! k! k# `, A+ }for i=1:round(tf/dt)+1/ |: @0 ]! j3 T" J! @4 K% Z
t(i)=dt*(i-1)0 m4 K7 G% q$ }
y(:,i)=expm(A*t(i))*y0;4 h" n: a3 t0 L! t2 A- s; Y- U
end# @7 P* C; c$ |/ g
subplot(2,1,1),plot(t,y(1,),grid 3 Q+ i+ n( S4 B( G8 Q
subplot(2,1,2),plot(t,y(2,),grid
8 m% U# k. U5 k[p,lamda]=eig(A)+ J8 G5 l0 @0 P3 \
2 Z$ a* S$ d- ` a3 v% K: B* S9 N% ?- p' m: c
% g+ p- l8 ]- O4 s3 V* G- ?/ m( @+ C( v
lamda =1 j+ s" @0 D t" ?# b* H
Columns 1 through 23 }& ~4 d. l& a
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
3 A. @4 a7 G* N. o* o 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i! Q& J$ a, g$ |
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i# F# g+ S4 W* k* d& a
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
" `4 q/ I. W9 Q Columns 3 through 49 g& Z8 G8 Z, k' q) j% M
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
9 v# C* \: e% N3 d/ P2 i. C4 D% E4 @ 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
2 r; E" t2 ~$ y( u( n/ | -0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
8 M N& T9 K. `- b |& t- q 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
4 Y4 U9 G( x1 S" I- ?" s6 F4 t0 W; \. ^$ u# i. W5 w( t
5 W+ J% X1 X7 |. n1 r; B" Z, R( M) E, m
z6 j1 C; c& t. ]) l
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