matlab子空间迭代法求结构频率和振型
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
子空间迭代法求图示结构前2阶频率和振型
syms m k w;
K=[k -k 0 0 0
-k 2*k -k 0 0
0 -k 2*k -k 0
0 0 -k 2*k –k
0 0 0 -k 2*k]; %刚度矩阵
M=[m 0 0 0 0;0 m 0 0 0;0 0 m 0 0;0 0 0 m 0;0 0 0 0 m] ; %质量矩阵
fi1=m/k*[ 15, 5; 14, 4;12, 3;9, 2;5,1] %迭代法迭代一次后得fai1作为初始向量
fi10=m/k*[15,14,12,9,5;5,4,3,2,1] %fai1的转置
K0=fi10*K*fi1 % K*
M0=fi10*M*fi1 %M*
C=K0-w^2*M0 %频率方程矩阵
det(C) %得到5*(10*k^2 - 136*k*m*w + 161*m^2*w^2))/k^2
solve('(5*(10*k^2 - 136*k*m*w + 161*m^2*w^2))/k^2=0','w')
%得到w^2= (68*k + 3014^(1/2)*k)/(161*m)
=((68 + 3014^(1/2))/(161))*k/m=122.8999*k/m
w^2= (68*k - 3014^(1/2)*k)/(161*m)
=((68 -3014^(1/2))/(161))*k/m=13.1001*k/m
w= ((68*k + 3014^(1/2)*k)/(161*m))^(1/2)
D=[ (55*m^2)/k - (671*m^3*w^2)/k^2, (15*m^2)/k -
(190*m^3*w^2)/k^2;(15*m^2)/k - (190*m^3*w^2)/k^2, (5*m^2)/k -
(55*m^3*w^2)/k^2]
factor(D)
E=[ ((- (671*3014^(1/2))/161 - 36773/161)*m^2)/k, ((- (190*3014^(1/2))/161 - 10505/161)*m^2)/k; ((- (190*3014^(1/2))/161 - 10505/161)*m^2)/k, ((- (55*3014^(1/2))/161 - 2935/161)*m^2)/k]*k/m^2
E=[ (- (671*3014^(1/2))/161 - 36773/161), (- (190*3014^(1/2))/161 - 10505/161);- ((190*3014^(1/2))/161 - 10505/161),(- (55*3014^(1/2))/161 - 2935/161)]
det(E)
E=[
E =[ -4021663268999919/8796093022208, -4575275808784111/35184372088832; -4575275808784111/35184372088832, -2602548662863391/70368744177664]
rref(E)
[ 885603878381/2199023255552,
-4043870143041/8796093022208;-4043870143041/8796093022208, 73860949044947/140737488355328]/885603878381*2199023255552
1.0000 -1.1416; -1.1416 1.30325056
1/1.1416
[15 5;14 4;12 3;9 2;5 1]*[1 1;0.8760 -3.5162]
[ 19.3800 17.5040 14.6280 10.7520 5.8760 ]/ 19.3800
[-2.5810 -0.0648 1.4514 1.9676 1.4838]/(-2.5810)
wli=4.730
A=[0 1 0 1;1 0 1 0;sin(rl) cos(rl) sinh(rl) cosh(rl);cos(rl) -sin(rl) cosh(rl) sinh(rl)]