MATLAB for Vibration Data Processing

Engineering Task

Processing vibration test data in MATLAB to extract frequency content, PSD, frequency response functions and modal parameters.

FFT and PSD

% FFT of time history:
N = length(t);
fs = 1 / (t(2) - t(1));
f = (0:N-1) * fs / N;
X = fft(x) / N;
magnitude = abs(X(1:N/2));
freq = f(1:N/2);

% PSD using Welch method:
[pxx, f_psd] = pwelch(x, hanning(Nfft), Noverlap, Nfft, fs);

Frequency Response Function

• Use tfestimate for H1 estimator (output/input) — standard for modal testing
• Use invfreqz for fitting transfer functions from FRF data
• Check coherence (cohere) — low coherence indicates noise or nonlinearity
• Plot Bode (bodeplot) for amplitude and phase versus frequency

Damping Estimation

• Half-power bandwidth: measure peak width at -3 dB points
• Logarithmic decrement: from free vibration decay
• Curve fitting: fit a single-DOF transfer function to each modal peak
• Verify damping values are physically reasonable — not default 2%

Related Knowledge

• Modal Analysis Review Checklist
• Damping Assumption Review Checklist