FFT - find frequency from a time history of displacement

%% inputs: time, displacement, lift and drag coefficents
% author: guofei, kaiming ai 
% output: normalised displacement vs time
clear;
clc;
%% read data
data=xlsread(‘gap0.005ur7.xlsx‘);
A1=data(800:4233,1); % time on one cycle
A2=data(800:4233,2); % displacement
A3=data(800:4233,3); % lift
A4=data(800:4233,4); % drag
% plot(A1,A2)
%% plot data
figure(1);
U=1.1686;       %free stream velocity
fig_hei=0.28;
fig_wei=0.9;
lef_cor_x=0.08;
lef_cor_y=0.1;

% sub-figure1: drag history
subplot(3,1,1,‘position‘, [lef_cor_x lef_cor_y+fig_hei+fig_hei fig_wei fig_hei])
plot(A1*U/0.1,A4,‘b-‘);
ylabel(‘\itC_{D}‘,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘);
set(gca,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘)
axis([20,400,-inf,inf])
set(gca,‘xticklabel‘,[])
box off
ax2 = axes(‘Position‘,get(gca,‘Position‘),...
           ‘XAxisLocation‘,‘top‘,...
           ‘YAxisLocation‘,‘right‘,...
           ‘Color‘,‘none‘,...
           ‘XColor‘,‘k‘,‘YColor‘,‘k‘);
set(ax2,‘YTick‘, []);
set(ax2,‘XTick‘, []);
box on
%sub-figure2: Cl, lift coefficient history
subplot(3,1,2,‘position‘, [lef_cor_x lef_cor_y+fig_hei fig_wei fig_hei])
plot(A1*U/0.1,A3,‘r-‘);
ylabel(‘\itC_{l}‘,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘);
set(gca,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘)
axis([20,400,-inf,inf])
set(gca,‘xticklabel‘,[])
box off
ax2 = axes(‘Position‘,get(gca,‘Position‘),...
           ‘XAxisLocation‘,‘top‘,...
           ‘YAxisLocation‘,‘right‘,...
           ‘Color‘,‘none‘,...
           ‘XColor‘,‘k‘,‘YColor‘,‘k‘);
set(ax2,‘YTick‘, []);
set(ax2,‘XTick‘, []);
box on
%subplot 3: A/D, normalised displacement history
subplot(3,1,3,‘position‘, [lef_cor_x lef_cor_y fig_wei fig_hei])
plot(A1*U/0.1,A2/0.1,‘r-‘);
ylabel(‘\itA/D‘,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘);
xlabel(‘\ittU/D‘,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘);
set(gca,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘)
axis([20,400,-inf,inf])
box off
ax2 = axes(‘Position‘,get(gca,‘Position‘),...
           ‘XAxisLocation‘,‘top‘,...
           ‘YAxisLocation‘,‘right‘,...
           ‘Color‘,‘none‘,...
           ‘XColor‘,‘k‘,‘YColor‘,‘k‘);
set(ax2,‘YTick‘, []);
set(ax2,‘XTick‘, []);
box on
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FFT
Data_FFT=[A2,A3,A4];
S=[Data_FFT(:,1)-mean(Data_FFT(:,1)),Data_FFT(:,2)-mean(Data_FFT(:,2)),Data_FFT(:,3)-mean(Data_FFT(:,3))];
Fs=200;% sample freq
N=9000;% number of sample
t=[0:1/Fs:N/Fs];
Y=fft(S,N);
Ayy=(abs(Y));
%Ayy=Ayy/(N/2);
Ayy_1=Ayy(:,1);  % fft of dis
Ayy_2=Ayy(:,2);  % fft of CL
Ayy_3=Ayy(:,3);
F=([1:N]-1)*Fs/N;  % frequency
%%%%%%%%
% find peak frequency corresponding to max FFT of dis, Cl, Cd
%%%%%%%%
XIndex1 = find(Ayy_1 == max(Ayy_1),1, ‘first‘);
Ayy_1_max = max(Ayy_1);
f_dis = F(XIndex1);  % 1st harmonic of displacement
%%%%%%%%%% 
% plot 2
%%%%%%%%%%%%%
figure(2);
%FFT of cd
subplot(3,1,1,‘position‘, [lef_cor_x lef_cor_y+fig_hei+fig_hei fig_wei fig_hei])
plot(F(1:N/2),Ayy_3(1:N/2),‘b-‘,‘linewidth‘,2);
ylabel(‘\itAmplitude‘,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘);
set(gca,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘)
axis([0,10,0,inf])
set(gca,‘xticklabel‘,[])
box off
ax2 = axes(‘Position‘,get(gca,‘Position‘),...
           ‘XAxisLocation‘,‘top‘,...
           ‘YAxisLocation‘,‘right‘,...
           ‘Color‘,‘none‘,...
           ‘XColor‘,‘k‘,‘YColor‘,‘k‘);
set(ax2,‘YTick‘, []);
set(ax2,‘XTick‘, []);
box on
%FFT of cl
subplot(3,1,2,‘position‘, [lef_cor_x lef_cor_y+fig_hei fig_wei fig_hei])
plot(F(1:N/2),Ayy_2(1:N/2),‘b-‘,‘linewidth‘,2);
ylabel(‘\itAmplitude‘,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘);
set(gca,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘)
axis([0,10,0,3e3])
set(gca,‘xticklabel‘,[])
box off
ax2 = axes(‘Position‘,get(gca,‘Position‘),...
           ‘XAxisLocation‘,‘top‘,...
           ‘YAxisLocation‘,‘right‘,...
           ‘Color‘,‘none‘,...
           ‘XColor‘,‘k‘,‘YColor‘,‘k‘);
set(ax2,‘YTick‘, []);
set(ax2,‘XTick‘, []);
box on
% subplot 3 : dis
subplot(3,1,3,‘position‘, [lef_cor_x lef_cor_y fig_wei fig_hei])
plot(F(1:N/2),Ayy_1(1:N/2),‘b-‘,‘linewidth‘,2);
xlabel(‘\itf‘,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘);
ylabel(‘\itAmplitude‘,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘);
set(gca,‘fontsize‘,20,‘fontname‘,‘Times New Roman‘)
axis([0,10,0,100])
box off
ax2 = axes(‘Position‘,get(gca,‘Position‘),...
           ‘XAxisLocation‘,‘top‘,...
           ‘YAxisLocation‘,‘right‘,...
           ‘Color‘,‘none‘,...
           ‘XColor‘,‘k‘,‘YColor‘,‘k‘);
set(ax2,‘YTick‘, []);
set(ax2,‘XTick‘, []);
box on
%% mean value of Cd
mean_Cd = mean(A4)
%% rms_Cd
rms_Cd = rms(A4)
%% rms_cl
rms_Cl = rms(A3)
%% displacement
A2_mean = A2(A2>0.06);
s = sum(A2_mean);
l = length(find(A2>0.06));
dis_ave = s/l;
%% RMS of displacement, max displacement
Rms = rms(A2);
dis = Rms*(2)^0.5
max_dis = max (A2)
K = F‘;
C = data(:,1)*U/0.1;