matlab子空间迭代法求结构频率和振型.doc

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1、子空间迭代法求图示结构前2阶频率和振型symsmkw;K=[k-k000-k2*k-k000-k2*k-k000-k2*k–k000-k2*k];%刚度矩阵M=[m0000;0m000;00m00;000m0;0000m];%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*

2、w+161*m^2*w^2))/k^2solve('(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/mw^2=(68*k-3014^(1/2)*k)/(161*m)=((68-3014^(1/2))/(161))*k/m=13.1001*k/mw=((68*k+3014^(1/2)*k)/(161*m))^(1/2)D=[(55*m^2)/k-(671*m^3*w^2)/k^2,

3、(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^2E=[(-(671*3014^(1/

4、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=[-99919/08,-84111/832;-84111/832,-63391/664]rref(E)[1/52,-41/08;-41/08,947/5328]/1*521.0000-1.1416;-1.14161.1/1.1416[155;144;123;92;51]*[11;0.8760-3.5162][19

5、.380017.504014.628010.75205.8760]/19.3800[-2.5810-0.06481.45141.96761.4838]/(-2.5810)wli=4.730A=[0101;1010;sin(rl)cos(rl)sinh(rl)cosh(rl);cos(rl)-sin(rl)cosh(rl)sinh(rl)]