relativemotion.m

This code is used for modeling frequency response and phase change of accelerometer.

% calculate the natural frequency of the system
% caculate the stiffness
E1=2.05e11;
E2=7.31e10;
a=0.0005
b=0.0045
w=0.0007;
h=0.002;
I1=w*h.^3/12;% the moment of inertia of the cantilever
r=0.0000625;% the radius of fiber
A=pi*r^2; % the cross-section area of the fiber
l1=0.015;% unit is m
l2=0.011;% unit is m
k1=3*E1*I1/l1^3; % beam's stiffness
k2=E2*A/l2; %fiber's stiffness
k=k1+k2;
m=0.004;
Wn=sqrt(2*k/m);
fn=Wn/2/pi;
w=0.1:2*pi*5:2*pi*(fn+100);
for epsiro=0.05:0.05:1; % damping ratio
    c=w/Wn; % frequency ratio
    Ar=c.^2./sqrt((1-c.^2).^2+(2.*epsiro.*c).^2); % Amplitude ratio
    phase=atan(2.*epsiro./(1-c.^2))*360/2/pi;
    % if the angle is less than 0,then plus 180
    A=phase<0;
    [r c]=find(A==1);
    phase(r,c)=phase(r,c)+180;
    % plot the dimensionless amplitude ratio
    subplot(1,2,1);
    hold on;
    plot(w/2/pi,20*log10(Ar./w.^2));
    xlabel(' frequency');
    ylabel('|Z|/(|Y|w^2)');
    grid on;
    hold off;
    %plot the phase angle of frequency response
    subplot(1,2,2);
    hold on;
    grid on;
    plot(w/2/pi,phase);
    xlabel('frequency');
    ylabel('phase angular');
    hold off;
end;