三自由度系统振动分析的实例
- %Calculate the natural frequencies,the normalized mode shapes and the FRFS
- clear
- close
- a=0.001;b=0.001;
- M=[100,0,0;0,100,0;0,0,100];
- K1=[2,-1,0;-1,2,-1;0,-1,2];
- K=1.0e+5*K1;
- C=a*M+b*K; %比例阻尼
- [V,D]=eig(K,M);
- for j=1:1:3
- omega(j)=sqrt(D(j,j));
- for k=1:1:3
- Y(k,j)=V(k,j)/V(3,j);
- end
- end
- omega
- Y
- w=0:0.1:70; %频率取值范围和步长
- H=zeros(701,3,3);
- for j=1:1:701
- Z=K-w(j)^2*M+w(j)*C*i; %动刚度矩阵
- HH=inv(Z); %频响函数矩阵
- H(j,:,:)=HH;
- end;
- Hr=real(H);Hi=imag(H);
- Habs=abs(H);Hang=(180/pi)*angle(H);
- figure(1)
- subplot(2,1,1),plot(w,Hr(:,1,1)),grid on
- title('实频曲线'),xlabel('\omega'),ylabel('Hr')
- subplot(2,1,2),plot(w,Hi(:,1,1)),grid on
- title('虚频曲线'),xlabel('\omega'),ylabel('Hi')
- figure(2)
- subplot(2,1,1),plot(w,Habs(:,1,1)),grid on
- title('幅频曲线'),xlabel('\omega'),ylabel('|H|')
- subplot(2,1,2),plot(w,Hang(:,1,1)),grid on
- title('相频曲线'),xlabel('\omega'),ylabel('\psi')
- figure(3)
- plot(Hr(:,1,1),Hi(:,1,1)),grid on
- title('乃奎斯特圆'),xlabel('Re(H)'),ylabel('Im(H)')
- %画跨点 的频响
- figure(4)
- subplot(2,1,1),plot(w,Hr(:,2,1)),grid on
- title('实频曲线'),xlabel('\omega'),ylabel('Hr')
- subplot(2,1,2),plot(w,Hi(:,2,1)),grid on
- title('虚频曲线'),xlabel('\omega'),ylabel('Hi')
- figure(5)
- subplot(2,1,1),plot(w,Habs(:,2,1)),grid on
- title('幅频曲线'),xlabel('\omega'),ylabel('|H|')
- subplot(2,1,2),plot(w,Hang(:,2,1)),grid on
- title('相频曲线'),xlabel('\omega'),ylabel('\psi')
- figure(6)
- plot(Hr(:,2,1),Hi(:,2,1)),grid on
- title('乃奎斯特圆'),xlabel('Re(H)'),ylabel('Im(H)')
- %画跨点 的频响
- figure(7)
- subplot(2,1,1),plot(w,Hr(:,3,1)),grid on
- title('实频曲线'),xlabel('\omega'),ylabel('Hr')
- subplot(2,1,2),plot(w,Hi(:,3,1)),grid on
- title('虚频曲线'),xlabel('\omega'),ylabel('Hi')
- figure(8)
- subplot(2,1,1),plot(w,Habs(:,3,1)),grid on
- title('幅频曲线'),xlabel('\omega'),ylabel('|H|')
- subplot(2,1,2),plot(w,Hang(:,3,1)),grid on
- title('相频曲线'),xlabel('\omega'),ylabel('\psi')
- figure(9)
- plot(Hr(:,3,1),Hi(:,3,1)),grid on
- title('乃奎斯特圆'),xlabel('Re(H)'),ylabel('Im(H)')
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