子空间迭代法 matlab,matlab子空间迭代法求结构频率和振型

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