mv_sample.m

特征值

%% Sample solution of the motor vibration problem
%% GEHW 2007
%% FreeMat 3.3
%%
%% Step 1:
%% Primitive lumped mass-spring model analysis
%%
clear
indx=1:4000;
%% Frequency: W - 1~400, Rotor speed: 1-3800 RPM
w_freq=indx/10;
rpm_motor=w_freq*60/2/3.14159;
%% 1 - Forces vectors
F_vect=[8.634e-3*w_freq.*w_freq;0*w_freq;0*w_freq];
%% 2 - K matrix
%%
Es=2.07E11;  %% Modulus of elasticity for steel
Ib=8.45E-3;   %% Moment of inertia of the beam cross section
Lb=9.144;     %% Beam length between support
%% Rotor bearing spring constants
k_e=1.75E08;
%% Combined vertical spring constant of the beams
%% Sample solution : replace k_e with 9E08 and run program again
k_b=96*Es*Ib/Lb/Lb/Lb;  %% primitive design
%% k_b=9E8;  %% Sample solution
%% Concrete support spring constant
k_s=1.166E9;
K_m=[k_e,-k_e,0;-k_e,k_e+k_b,-k_b;0,-k_b,k_b+k_s];
%% 3 - M matrix
%% Mass of motor rotor
m_r=4310;
%% Mass of stator
m_s=11100;
%% Mass of beam
m_b=8166;
M_m=[m_r,0,0;0,m_s+m_b/2,0;0,0,m_b/2];
%% 4 - MX"+KX=F   > IY+LY=G, L=inv(M_m)*K and G=inv(M_m)*F
L=inv(M_m)*K_m;
G=inv(M_m)*F_vect; %% not used, just list here
%% 5 - Apply eigenvalue and eigenvector technique. calculate Y of different natual frequncies
[phi,eigv]=eig(L);
phi_t=transpose(phi);
Kappa=phi_t*K_m*phi;
F_x=phi_t*F_vect;
Y(1,:)=F_x(1,:)/Kappa(1,1)./(1-w_freq.*w_freq/eigv(1,1));
Y(2,:)=F_x(2,:)/Kappa(2,2)./(1-w_freq.*w_freq/eigv(2,2));
Y(3,:)=F_x(3,:)/Kappa(3,3)./(1-w_freq.*w_freq/eigv(3,3));
%% 6 - Restore to X,  X=phi*Y
X_p=phi*Y;
%% 7 - Output to graphics
%% displacement of mass 1
figure;
plot(rpm_motor,X_p(1,:));
ylim([-2E-5,2E-5]);
xlim([1,4000]);
grid on;
title('Mass #1');
xlabel('Motor Speed (RPM)');
ylabel('Peak Vibration Amplitude (m)');
figure;
plot(rpm_motor,X_p(2,:));
ylim([-2E-5,2E-5]);
xlim([1,4000]);
grid on;
title('Mass #2');
xlabel('Motor Speed (RPM)');
ylabel('Peak Vibration Amplitude (m)');
figure;
plot(rpm_motor,X_p(3,:));
ylim([-2E-5,2E-5]);
xlim([1,4000]);
grid on;
title('Mass #3');
xlabel('Motor Speed (RPM)');
ylabel('Peak Vibration Amplitude (m)');