% 无阻尼二自由系统固有频率的程序 20180401A+ g j6 N$ |7 K9 l$ I2 `3 f
m1=100;m2=100;k1=200;k2=400;%
2 D F6 m+ x# ]. I5 w1 F* yc1=0;c2=0;
- c7 i$ C. a; X$ x1 \" O5 I! gx0=[1;0];xd0=[0;0];tf=50;dt=0.1;
- ~; R! f$ n1 M8 uM=[m1,0;0,m2];k=[k1+k2,-k2;-k2,k2];' ^6 B$ Y: \4 T( x* ]+ X; H6 U
c=[c1+c2,-c2;-c2,c2];* N! P5 u) u2 ^
A=[zeros(2,2),eye(2);-M\k,-M\c];
5 F, f, H3 z# t% t) e: H$ ny0=[x0;xd0];4 K* z3 R( l4 M$ @/ I1 t w% P1 @
for i=1:round(tf/dt)+1
0 u+ R3 G8 B) R) o( `) E& A8 W2 \8 o t(i)=dt*(i-1)" k% l7 e- S3 d& J0 i
y(:,i)=expm(A*t(i))*y0;" K6 R' _# n5 r+ Y2 F' E
end2 t# a1 h" c0 m# {
subplot(2,1,1),plot(t,y(1, ),grid 6 Y9 X& y" `1 Y. G0 X
subplot(2,1,2),plot(t,y(2,),grid
! Z8 d; X- N2 T4 H3 q+ j# P4 ~[p,lamda]=eig(A)
/ `9 [5 _" f! G$ |, |' }( u1 k. m0 S+ s5 _: M- d- G, ^* f* c" f
f+ q0 J. |8 o. O4 m. A) |. F4 N8 y, @
) I* C r& w) ~/ ]5 Dlamda =: {# O0 Z! e. L3 ]% P& ?* A
Columns 1 through 2
. f' X7 [. v9 d 0.000000000000000 + 3.020447918044219i 0.000000000000000 + 0.000000000000000i
$ n# d4 x# R, F. l5 K 0.000000000000000 + 0.000000000000000i 0.000000000000000 - 3.020447918044219i
- ~: i! L( f4 P' a4 f ^& h1 h6 t 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
' Q5 F7 s* k4 S) n 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i) x2 k( i0 w3 x! |
Columns 3 through 4
8 J* B, x" @9 Y1 X/ l& t- w: `' u 0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i) Z4 C- \8 J$ d" M2 j- R* U# f: g6 z
0.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i& R: Q. ]8 q$ b7 s
-0.000000000000000 + 0.936426384924271i 0.000000000000000 + 0.000000000000000i1 B/ r3 [- m: r( I8 j$ {2 p
0.000000000000000 + 0.000000000000000i -0.000000000000000 - 0.936426384924271i
0 p; w& [- i4 u; B, R; i/ `& I6 a+ v2 |; Y9 e8 c- A2 b
. N% E* U0 Y8 s7 @- u
f% ?. d4 O: U. |$ G5 \3 V: S* \+ ~
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发表于 2018-4-16 19:41:12
