SDOF time history analysis

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Abed Eltablawy
Abed Eltablawy 2021-5-3
评论： Mathieu NOE 2025-7-4
how I can write a code to do time history analysis for a specific ground motion

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Mathieu NOE
Mathieu NOE 2025-4-3
Ran in:
if you need a code to perform some spectral analysis and integration (to get velocity and displacement)
you can try this :
filename = "bcj.xlsx";
data = readmatrix(filename);
acc = data(6:end,2); % select here which channel to process
dt = 0.01;
fs = 1/dt; % sampling rate
t = (0:numel(acc)-1)*dt;
acc = acc/100; % convert from cm/s² to m/s²
figure(1)
plot(t,acc)
ylabel('Accel [m/s²]')
xlabel('Time [s]')
title(' Acceleration')
% fft of the Acceleration signal
L = length(acc); % Length of signal
NFFT = 2^nextpow2(L); % Next power of 2 from length of y
accSpectrum = fft(acc, NFFT)/L;
f = fs/2*linspace(0,1,NFFT/2+1);
accSpectrum = abs(accSpectrum(1:NFFT/2+1));
figure(2);
semilogx(f, accSpectrum);
title('FFT of acceleration')
xlabel('Frequency (Hz)')
ylabel('Amplitude')
hold on
% add findpeaks to display dominant frequencies
NP = 20;
[PKS,LOCS] = findpeaks(accSpectrum,f,'SortStr','descend','NPeaks',NP);
plot(LOCS,PKS,'dr');
for ck = 1:NP
text(LOCS(ck)*1.1,PKS(ck)*1.2,[num2str(LOCS(ck),3) 'Hz']);
end
hold off
●
% main code
fc = 0.25; % Hz , this cut off frequency must be below first significant peak frequency in your signal
[vel,displ] = double_int2(acc,fc,fs); % double integration (cumtrapz) with high pass filtering
figure(3)
plot(t,vel)
ylabel('Vel. [m/s]')
xlabel('Time [s]')
title('Estimated Velocity')
figure(4)
plot(t,displ)
ylabel('Dis. [m]')
xlabel('Time [s]')
title('Estimated Displacement')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [vel,displ] = double_int2(x,fc,Fs)
dt = 1/Fs;
% DC blocking filter (discrete)
fn = fc/(Fs/2); % normalized cutt off frequency
p = (sqrt(3) - 2*sin(pi*fn))/(sin(pi*fn) + sqrt(3)*cos(pi*fn));
b = [1 -1]; % (numerator)
a = [1 -p]; % (denominator)
accel = filtfilt(b,a,x); % filter the test data with filtfilt
% accel to velocity integration
vel = dt*cumtrapz(accel); % integration
vel = filtfilt(b,a,vel); % detrend data with filtfilt
% velocity to displ integration
displ = dt*cumtrapz(vel); % integration
displ = filtfilt(b,a,displ); % detrend data with filtfilt
end

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