Ground Vibration Testing

Ground Vibration Testing (flight-test-operations/flutter/ground-vibration-testing)

Use when the task is a ground vibration test (GVT) for flutter clearance: measuring the structural natural frequencies, mode shapes, and damping of the aircraft on the ground before flight, and checking the measured data quality before the results feed the flutter clearance model.

Domain quick reference

• Purpose: a GVT measures the structural natural frequencies, mode shapes, and damping of the airframe on the ground before flight. The measured modes update and validate the structural dynamic model that the flutter clearance analysis is built on, so the test data quality gates everything downstream.
• Excitation methods: electrodynamic shakers (attached with stingers, force gages in line), impact hammers (broadband impulse, light structure friendly), sine sweep (slowly swept single sine, high signal-to-noise at resonance), and random excitation (broadband, fast, low peak force). Each excites the structure at the drive point and the response is measured at the accelerometer stations.
• Frequency response function: H(f) = A(f) / F(f), the response acceleration spectrum over the excitation force spectrum. The FRF magnitude peaks at the natural frequencies and the phase flips through the resonance; the FRF is the primary data product of the test.
• Frequency resolution: df = sample_rate / n_samples, the FFT line spacing in Hz. With typical damping below a few percent, df must be fine enough that the half-power band of each mode spans several lines, or damping is overestimated.
• Half-power bandwidth damping: zeta = (f2 - f1) / (2 * fn), with fn the natural frequency and f1, f2 the frequencies where the FRF magnitude has fallen to 1/sqrt(2) of the peak value. Damping is dimensionless; zeta below about 0.03 to 0.05 is typical for airframe modes.
• Mode extraction: peak picking finds candidate modes from FRF magnitude peaks, circle fit fits a circle to the FRF in the Nyquist plane for a refined natural frequency and damping, and curve fitting (multi-DOF, e.g. rational fraction polynomial) separates closely spaced modes that overlap in frequency.
• Mode shapes and mass normalization: the mode shape is the relative displacement at each accelerometer station for a given mode; mass normalization scales the shape so the generalized mass is unity, which lets the measured mode be compared directly with the analysis model mode (via the MAC) and used for flutter correlation.
• Test setup: accelerometers placed to capture the expected mode shapes (no station at a node line of a mode of interest), the structure suspended on soft bungee or air springs so the rigid body modes sit well below the first elastic mode and do not contaminate the band of interest.
• Quality checks: coherence gamma^2 in [0, 1] near unity (0.9 or better) means the response is linearly driven by the input; reciprocity H_ij = H_ji within a few percent holds for a linear time-invariant structure. Low coherence or broken reciprocity flags noise, leakage, nonlinearity, or a bad transducer.
• GVT-to-flight correlation: the mass-normalized measured modes are compared with the analysis model (frequency differences typically within a few percent, MAC above about 0.9 for well-correlated modes); the correlated model then carries the flutter clearance.

Workflow

1. Plan the setup: choose the excitation method, place the accelerometers on the structure, and suspend the aircraft on soft supports so the rigid body modes stay below the first elastic mode.
2. Check the acquisition band with frequency_resolution(sample_rate, n_samples) and confirm the line spacing resolves the expected half-power bands.
3. Measure the FRFs and screen every FRF with coherence_verdict (coherence) and reciprocity_check(h12, h21); discard or redo data that fails.
4. Extract the modes: locate candidate peaks with peak_pick_verdict(frf_peak, threshold), then refine each candidate with the half-power bandwidth or a curve fit.
5. Estimate the modal damping of each accepted mode with half_power_damping(f1, f2, fn) and record the mode shapes from the FRF responses at the stations.
6. Mass-normalize the mode shapes and compare the count with the analysis model using mode_count_verdict(peaks, expected); a mismatch means modes are missed, split, or not in the band.
7. Correlate the measured modes with the model (frequency differences, MAC) and feed the correlated model into the flutter clearance.

Pitfalls

• Damping from a too-coarse frequency resolution: if the half-power band spans fewer than a few FFT lines the bandwidth is overestimated and zeta comes out too high; check frequency_resolution before trusting the damping.
• Peak picking on noise: an FRF peak below the threshold is not a mode; forcing every peak to be a mode inflates the mode count and corrupts the correlation.
• Ignoring coherence and reciprocity: low coherence or broken reciprocity means the FRF is not a clean linear measurement; gate the data before extracting modes.
• Accelerometer on a node line: a station placed at a node of a mode of interest records no response for that mode and the mode shape looks wrong; check the analytical node locations when placing the stations.
• Rigid body modes in the band: stiff suspension raises the rigid body frequencies toward the first elastic mode and contaminates it; the supports must keep them well separated.
• Half-power points not bracketing the natural frequency: feeding f1 and f2 that do not straddle fn (or any non-positive frequency) raises ValueError; use the actual 1/sqrt(2) crossings, not arbitrary points.
• Confusing found and expected mode counts: the mode count verdict compares detected peaks with the model expectation in the test band; extra peaks (noise, rigid body) and missing peaks (node placement, weak excitation) both fail the check and need investigation, not acceptance.

Behavior contract (gate 3)

The half-power damping, peak picking, frequency resolution, mode count, reciprocity, and coherence logic is exercised by the gate 3 contract test: scripts/test_ground_vibration_testing.py against scripts/ground_vibration_testing_logic.py (stdlib unittest, offline). Run: python3 scripts/test_ground_vibration_testing.py

Compliance

• Standards referenced, not reproduced: FAR-25 is US government work (public domain) and CS-25 is a free EASA download; the GVT methodology (excitation, FRF measurement, mode extraction, half- power damping, quality checks, model correlation) sits in the flutter clearance context of the FAR 25.629 / CS 25.629 certification practice as common structural dynamics knowledge, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.