Reconstruct continous displacement function from FFT

I have the time history of the displacement in X and Y of a series of points on a cantilever beam. What i'm trying to do is reconstruct a function of time of said displacement (one for each direction) for every point. To do so i'm thinking to sum a series of sinusoids deriving from an FFT done on every point once for x and once for y. I cannot obtain the desired function, it doesn't fit the original signal. J=91 refers to the 91st point, in the center of the beam, used to validate the method that later has to be expanded on every point.

clc
close all
clear all
[y1,Fs1]=audioread("video test 1.mp4");
v1=VideoReader("video test 1.mp4");
tf_1=v1.duration;  %durata video che leggo in v1
y1mono=mean(y1')';
[y2,Fs2]=audioread("video test 2.mp4");
v2=VideoReader("video test 2.mp4");
tf_2=v2.duration;  %durata video che leggo in v2
y2mono=mean(y2')';
if Fs1~=Fs2
    if Fs2>Fs1
        y2mono=resample(y2mono,Fs1,Fs2);
    else
        y1mono=resample(y1mono,Fs2,Fs1);
    end
end
time1=linspace(0,tf_1,length(y1mono));
time2=linspace(0,tf_2,length(y2mono));
figure(1)
subplot(2,1,1);
hold on 
grid minor
title(sprintf('Segnali separati'))
xlabel('Time [s]')
ylabel('Volume')
plot(time1,y1mono,'r')
plot(time2,y2mono,'g')
grid minor
[y1_all,y2_all,D]=alignsignals(y1mono,y2mono,Method="xcorr");
time_delay=abs(D)/Fs2;
time_1=linspace(0,tf_2,length(y1_all));
time_2=linspace(0,tf_2,length(y2_all));
subplot(2,1,2)
hold on
grid minor
title(sprintf('Segnali allineati con Alignsignal'))
xlabel('Time [s]')
ylabel('Volume')
plot(time_1,y1_all,'r')
plot(time_2,y2_all,'b')
grid minor
%%
load('DIC2DRefResults_C_NaN.mat');
load('DIC2DDefResults_C_NaN.mat');
Fs_1=v1.FrameRate;                                   
Fs_2=v2.FrameRate;                                   
NPoints=448;
NFrame_1=700;
NFrame_2=700;
t1=linspace(1,NFrame_1,NFrame_1)*(1/Fs_1);
t2=linspace(1,NFrame_2,NFrame_2)*(1/Fs_2);
for j=1:NPoints
    for i=1:length(t1)                              
        RefX(j,i)=DIC2DrefResults.Points{i}(j,1);
        RefY(j,i)=DIC2DrefResults.Points{i}(j,2);
    end
end
%%
tol_xr=0;
tol_yr=0;
k=25;
for i=1:NPoints
    RefX_cl{i}=RefX(i,:);
    RefY_cl{i}=RefY(i,:);
    Mean_Xr{i}=mean(RefX_cl{i});
    Mean_Yr{i}=mean(RefY_cl{i});
    RefX_cl{i}=RefX_cl{i};
    RefY_cl{i}=RefY_cl{i};
    
    Displ_xr{i}=fft(RefX_cl{i});
    Displ_xr{i}(1,1)=0;
    Displ_yr{i}=fft(RefY_cl{i});
    Displ_yr{i}(1,1)=0;
    asse_freq_xr{i}=Fs_1/NFrame_1*(0:NFrame_1-1);
    asse_freq_yr{i}=Fs_1/NFrame_1*(0:NFrame_1-1);
    Displ_xr{i}(abs(Displ_xr{i})<tol_xr)=0;                                %fase della fft dopo rimozione picchi
    Displ_yr{i}(abs(Displ_yr{i})<tol_yr)=0;                                %fase della fft dopo rimozione picchi
    
    X_r{i}=fftshift(Displ_xr{i});
    Y_r{i}=fftshift(Displ_yr{i});
    theta_xr{i}=angle(Displ_xr{i});
    theta_yr{i}=angle(Displ_yr{i});
    freq_shift_xr{i}=linspace(-Fs_1/2,Fs_1/2,NFrame_1);
    freq_shift_yr{i}=linspace(-Fs_2/2,Fs_2/2,NFrame_1);
    IFT_yr{i}=ifft(Displ_yr{i});
    IFT_xr{i}=ifft(Displ_xr{i});
    
    [MPks_xr{i},Mlocs_xr{i}]=maxk(abs(Displ_xr{i}),k);
    [MPks_yr{i},Mlocs_yr{i}]=maxk(abs(Displ_yr{i}),k);
end
j=91;
x{j}=@(t) Mean_Xr{j} + 0*t;
for i=1:k
    onda_x=@(t) (2*(MPks_xr{j}(i))/NFrame_1)*cos(2*pi*asse_freq_xr{j}(Mlocs_xr{j}(i))*t+theta_xr{j}(Mlocs_xr{j}(i)))+(2*(MPks_xr{j}(i))/NFrame_1)*sin(2*pi*asse_freq_xr{j}(Mlocs_xr{j}(i))*t+theta_xr{j}(Mlocs_xr{j}(i))+pi/2);    
    x{j}=@(t) x{j}(t)+onda_x(t);
end
j=91;
y{j}=@(t) Mean_Yr{j} + 0*t;
for i=1:k
    onda_y=@(t) (2*(MPks_yr{j}(i))/NFrame_1)*cos(2*pi*asse_freq_yr{j}(Mlocs_yr{j}(i))*t+theta_yr{j}(Mlocs_yr{j}(i)))+(2*(MPks_yr{j}(i))/NFrame_1)*sin(2*pi*asse_freq_yr{j}(Mlocs_yr{j}(i))*t+theta_yr{j}(Mlocs_yr{j}(i))+pi/2);    
    y{j}=@(t) y{j}(t)+onda_y(t);
end
%%
figure(2)
plot(t1,RefX_cl{91},'b')
title('Displacement X :camera 1')
xlabel('Time [s]')
ylabel('Amplitude')
hold on
grid minor
figure(3)
plot(t1,RefY_cl{91},'b')
title('Displacement Y :camera 1')
xlabel('Time [s]')
ylabel('Amplitude')
hold on
grid minor
figure(4)
subplot(2,1,1);
plot(freq_shift_xr{91},abs(X_r{91}));
xlim([0 60])
title('FFT of X displacement : camera 1 ');
xlabel('Frequency [Hz]')
ylabel('Amplitude')
grid minor
subplot(2,1,2);
plot(freq_shift_xr{91},theta_xr{91}/pi);
title('Phase : camera 1')
xlabel('Frequency [Hz]')
ylabel('Phase  [1/pi]')
%xlim([0 60])
grid minor
figure(6)
subplot(2,1,1);
plot(freq_shift_yr{91},abs(Y_r{91}));
xlim([0 60])
title('FFT of Y displacement: camera 1')
xlabel('Frequency [Hz]')
ylabel('Amplitude')
grid minor
subplot(2,1,2);
plot(freq_shift_xr{91},theta_yr{91}/pi);
title('Phase :camera 1')
xlabel('Frequency [Hz]')
ylabel('Phase  [1/pi]')
%xlim([0 60])
grid minor
%%
figure(7)
plot(t1,IFT_xr{91}+Mean_Xr{91})
title('Inverse fourier transform X : camera 1')
xlabel('Time [s]')
ylabel('Amplitude')
grid minor
figure(8)
plot(t1,IFT_yr{91}+Mean_Yr{91})
title('Inverse fourier transform Y : camera 1')
xlabel('Time [s]')
ylabel('Amplitude')
grid minor
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%555
%%
for j=1:NPoints
    for i=1:length(t1)                              
        DefX(j,i)=DIC2DdefResults.Points{i}(j,1);
        DefY(j,i)=DIC2DdefResults.Points{i}(j,2);
    end
end
tol_x_d=0;
tol_y_d=0;
t2=t2+time_delay;
for i=1:NPoints
    DefX_cl{i}=DefX(i,:);
    
    DefY_cl{i}=DefY(i,:);
    
    Mean_Xd{i}=mean(DefX_cl{i});
    Mean_Yd{i}=mean(DefY_cl{i});
    L2_xd{i}=length(DefX_cl{i});
    L2_yd{i}=length(RefY_cl{i});
    
    asse_freq_xd{i}=Fs_2/L2_xd{i}*(0:L2_xd{i}-1);
    asse_freq_yd{i}=Fs_2/L2_yd{i}*(0:L2_yd{i}-1);
    Displ_x_d{i}=fft(DefX_cl{i});
    Displ_y_d{i}=fft(DefY_cl{i});
    Displ_x_d{i}(1,1)=0;
    Displ_y_d{i}(1,1)=0;
    Displ_x_d{i}(abs(Displ_x_d{i})<tol_x_d)=0;                                %fase della fft dopo rimozione picchi
    X_d{i}=fftshift(Displ_x_d{i});
    theta_x_d{i}=angle(X_d{i});
    freq_shift_xd{i}=linspace(-Fs_2/2,Fs_2/2,L2_xd{i});
    Displ_y_d{i}(abs(Displ_y_d{i})<tol_y_d)=0;                                %fase della fft dopo rimozione picchi
    theta_y_d{i}=angle(Displ_y_d{i});
    Y_d{i}=fftshift(Displ_y_d{i});
    theta_y_d{i}=angle(Y_d{i});
    freq_shift_yd{i}=linspace(-Fs_2/2,Fs_2/2,L2_yd{i});
    IFT_xd{i}=ifft(Displ_x_d{i});
    IFT_yd{i}=ifft(Displ_y_d{i});
end
figure(9)
plot(t2,DefX_cl{91},'b')
title('Displacement X: camera 2')
xlabel('Time [s]')
ylabel('Amplitude')
hold on
grid minor
figure(10)
plot(t2,DefY_cl{91},'b')
title('Displacement Y: camera 2')
xlabel('Time [s]')
ylabel('Amplitude')
hold on
grid minor
figure(11)
subplot(2,1,1);
plot(freq_shift_xd{91},abs(X_d{91}));
xlim([0 60])
title('FFT of X displacement: camera 2');
xlabel('Frequency [Hz]')
ylabel('Amplitude')
grid minor
subplot(2,1,2);
plot(freq_shift_xd{91},theta_x_d{91}/pi);
title('Phase: camera 2')
xlabel('Frequency [Hz]')
ylabel('Phase  [1/pi]')
xlim([0 60])
grid minor
figure(12)
subplot(2,1,1);
plot(freq_shift_yd{91},abs(Y_d{91}));
xlim([0 60])
title('FFT of Y displacement: camera 2 ')
xlabel('Frequency [Hz]')
ylabel('Amplitude')
grid minor
subplot(2,1,2);
plot(freq_shift_yd{91},theta_y_d{91}/pi);
title('Phase:camera 2')
xlabel('Frequency [Hz]')
ylabel('Phase  [1/pi]')
xlim([0 60])
grid minor
%%
figure(13)
plot(t2,IFT_yd{91}+Mean_Yd{91})
title('Inverse fourier transform Y : camera 2')
xlabel('Time [s]')
ylabel('Amplitude')
grid minor
figure(14)
plot(t2,IFT_xd{91}+Mean_Xd{91})
title('Inverse fourier transform X : camera 2')
xlabel('Time [s]')
ylabel('Amplitude')
grid minor
%%
Def_int_y=interp1(t2,IFT_yd{91}+Mean_Yd{91},t1);
%%
figure(15)
plot(t1,IFT_yr{91}+Mean_Yd{91},'b',t1,Def_int_y,'r');                 % la media non è Yd ma Yr
figure(16)
plot(t1,x{91}(t1));
figure(17)
plot(t1,y{91}(t1));

[Catalytic]

I'm afraid we've no idea what you're talking about. It is an ocean of code that does not transparently describe either the mathematics of the problem, or the solution approach.