% 无阻尼二自由系统固有频率的程序 20180401A
5 a$ \/ B$ A# g1 k" O! tm1=100;m2=100;k1=200;k2=400;% : t2 R: D1 Y& ]
c1=0;c2=0;
/ O" X2 ~. k1 \' Z& S# x( q4 ux0=[1;0];xd0=[0;0];tf=50;dt=0.1;' B. M) R) {+ e; P
M=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];$ N, T7 J, ^* N2 c6 N
c=[c1+c2,-c2;-c2,c2];
5 D. w/ d; t) t4 m: \- a- }8 }; |A=[zeros(2,2),eye(2);-M\k,-M\c];
- V! O% o* l% a5 `, t" D- ]y0=[x0;xd0];* ]) d1 G, L; q3 K) _2 x1 S% ]5 q6 L4 Y( N
for i=1:round(tf/dt)+1
. ^* w* W, X! \- D t(i)=dt*(i-1)
/ Z6 K7 V) L3 Q5 L& x y(:,i)=expm(A*t(i))*y0;$ j/ ?5 _) D% A3 ?4 S
end
9 Q* D. ]) c* Q5 Q0 Z/ gsubplot(2,1,1),plot(t,y(1, ),grid
+ l+ l; Q7 u" P$ n& n# e, n0 ]" osubplot(2,1,2),plot(t,y(2,),grid
7 b, K( I, h6 s |9 [ L, D) j[p,lamda]=eig(A), V. Y8 e' W7 x9 {! \
; t8 H" H" G1 \4 D x" C; F: j( U
- G" G7 G Z4 `2 A
! E4 S% _3 R- a1 ]0 n% b
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lamda =+ k" |* ~* P! J* \7 l5 ?
Columns 1 through 2
, |! Z# w0 A; C" y3 P 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
+ }- m% s+ v/ L+ w6 Y( @ 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i0 L4 Z# [3 i% L. Z
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i2 ]+ A* g+ h' G$ V
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i7 V& T0 N/ p+ i( M, H5 ^
Columns 3 through 4
# j0 l- B4 ~5 I9 C, }# {, R9 g8 I 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
. r8 u4 |, k4 ^8 z 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i& z& t& a( n; x
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i
- {( @, f8 {' y6 X8 E 0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
& i' k- _3 B4 h; ]1 ~. D$ a- c1 U
3 Y O2 L' z; u6 y0 h" m
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发表于 2018-4-16 19:41:12
