临界转速.m

求解转子系统前三个临界转速和主振型的传递矩阵法

%求解转子系统前三个临界转速和主振型的传递矩阵法
clc
clear
%等截面轴参数
l1=０.１５;
d=0.04;
A=pi*d*d/4;
%轮盘参数
D=0.5;
h=0.025;
%盘轴材料参数（忽略轴的质量）
a=1;
u=0.3;
rou=7800;
E=2.0e11;
G=E/(2*(1+u));
I=pi*(d^4)/64;
K1=2.0e7;
v1=6*E*I/(a*G*A*l1*l1);
mi=rou*pi*D^2/4*h;%轮盘的集质量
Jp=mi*D^2/8;
Jd=Jp/2;
Ji=Jp-Jd;
%参数的数组形式
L=[l1 l1 l1 l1 l1 l1 l1 l1 l1 l1 l1 l1 l1 0 0];
M=[0 mi mi mi mi mi mi 0 0 0 0 0 mi mi 0];
K=[K1 0 0 0 0 0 0 K1 0 0 0 K1 0 0 0];
v=[v1 v1 v1 v1 v1 v1 v1 v1 v1 v1 v1 v1 v1 0 0];
J=[0 Ji Ji Ji Ji Ji Ji 0 0 0 0 0 Ji Ji 0];

k=0;
Tit=['第一阶频率的振型和弯矩图';'第二阶频率的振型和弯矩图';'第三阶频率的振型和弯矩图'];
for w=0:0.01:4000;
for i=1:15;
T(:,:,i)=[1+(L(i)^3)*(1-v(i))*(M(i)*w^2-K(i))/(6*E*I) L(i)+L(i)^2*J(i)*w^2/(2*E*I) L(i)^2/(2*E*I) L(i)^3*(1-v(i))/(6*E*I);

(L(i)^2)*(M(i)*w^2-K(i))/(2*E*I) 1+L(i)*J(i)*w^2/(E*I) L(i)/(E*I) L(i)^2/(2*E*I);

L(i)*(M(i)*w^2-K(i)) J(i)*w^2 1 L(i);

M(i)*w^2-K(i) 0 0 1];
end
H=T(:,:,1);
for i2=2:15;

H=T(:,:,i2)*H;
end

F=H(3,1)*H(4,2)-H(3,2)*H(4,1);

if F*(-1)^k < 0 %求解临界转速

k=k+1;

wi(k)=w;

w=wi(k)


ni(k)=wi(k)*30/pi;
end
end
for i1=1:3;

w=wi(i1);

for j=1:14;
T(:,:,j)=[1+(L(j)^3)*(1-v(j))*(M(j)*w^2-K(j))/(6*E*I) L(j)+L(j)^2*J(j)*w^2/(2*E*I) L(j)^2/(2*E*I) L(j)^3*(1-v(j))/(6*E*I);

(L(j)^2)*(M(j)*w^2-K(j))/(2*E*I) 1+L(j)*J(j)*w^2/(E*I) L(j)/(E*I) L(j)^2/(2*E*I);

L(j)*(M(j)*w^2-K(j)) J(j)*w^2 1 L(j);

M(j)*w^2-K(j) 0 0 1];
end
H=T(:,:,1);
for j=2:15;

H=T(:,:,j)*H;

end

b=-H(4,1)/H(4,2);

X(:,1)=([1 b 0 0]');

for n=2:16;

X(:,n)=T(:,:,n-1)*X(:,n-1);
%相邻两质点右边的传递关系

end 

for j1=1:15;

y(j1)=X(1,j1);

z(j1)=X(3,j1);

x(j1)=(j1-1)*l1;

end

y(16)=X(1,16);
x(16)=1.56;
z(16)=X(3,16);

y=y/max(abs(y));%归一化
z=z/max(abs(z));
subplot(3,1,i1)
plot(x,y,'b-',x,z,'r:')
title(Tit(i1,:))

xlabel('轴长'),ylabel('不平衡值')
axis([0,1.56,-1.2,1.2])
grid on
z;
end
legend('振型','弯矩')

ni
wi