% 无阻尼二自由系统固有频率的程序 20180401A5 J f; d5 o8 X, ]3 u& F, p( L
m1=100;m2=100;k1=200;k2=400;% 3 E4 g" a, w2 D6 l! N, L
c1=0;c2=0;
# ?2 D& |4 e( H# P$ S; Ox0=[1;0];xd0=[0;0];tf=50;dt=0.1;
5 W1 x5 `6 P* C; W0 p$ j, CM=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];! H3 }' L! r. K8 P2 \/ t: c1 P0 R: i$ B
c=[c1+c2,-c2;-c2,c2];% i4 u8 ^) K4 A' N* ~ I2 R# j; q$ T
A=[zeros(2,2),eye(2);-M\k,-M\c];1 l6 B0 f, J' Y7 O, f1 [9 [
y0=[x0;xd0];& c3 b$ d* o; e6 l; j3 a W+ f
for i=1:round(tf/dt)+1
) u3 }3 h' {5 z' B6 V t(i)=dt*(i-1)! r8 H5 x, j# e5 p" i0 ^
y(:,i)=expm(A*t(i))*y0;2 l, Z! D! a' K/ |
end9 h/ w9 u( ~6 |, ~& {
subplot(2,1,1),plot(t,y(1, ),grid # S* [- `! h; V7 U
subplot(2,1,2),plot(t,y(2,),grid
j+ J) {: y Z# c5 ?( |[p,lamda]=eig(A): I. E% ~0 V: y2 ~, a. F( a. M
! M$ f3 o, `9 J( u1 \# A% }6 G
. y8 i, e6 G2 t7 j7 f9 y8 B T' M8 P
$ Y2 Y% F3 O- r" j- I% l
& p: t( e% P( \lamda =7 T- h' E$ e% S& ^' E
Columns 1 through 2* r! Y; b0 ]* X3 U
0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
& A3 F# {; U" R- `% B0 {4 C 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i& T3 k3 o! u6 v0 a* `" L* l/ A" z
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
7 J; ?, P) |! F! f$ n" q% n3 g 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i7 Y7 n& u0 S! a% o1 j3 L3 {
Columns 3 through 4
# x+ u/ U' \# ]/ x& e 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
3 t( V. {8 ^ ?) B' @ 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i& w6 s$ d- ]' z
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
: q3 N5 s2 h3 r J! s 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i6 M" Y& P( k6 Q9 t5 W4 P
& i) R% N4 a) ~- r7 V* v" a, ^+ [/ ]
4 M. f# k9 w' R( y* N5 Q( j4 A9 M% ^+ z. `+ u# O) y8 S
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发表于 2018-4-16 19:41:12
