Application note | Modal testing
LDV Modal Analysis of an Aluminum Dome
Non-contact LDV mapping turns a lightweight aluminum dome into a practical modal test case. Six resonances from 20 Hz to 925 Hz were captured as full-field magnitude and phase maps, making nodal structure, circumferential order and frequency alignment visible without adding mass or wiring to the shell.
6
resonance modes resolved across the measured band
20-925 Hz
frequency range covered in the modal series
251
scan frames from phi = -6.0 degrees to +6.5 degrees in 0.05 degree steps
Coherence >= 0.71
frequency-response processing against the EHSC reference channel
Mode shapes become interpretable when amplitude and phase are seen together
Curved shells rarely behave like single-point systems. Useful modal data must show where motion concentrates, which regions move in or out of phase, and how nodal boundaries evolve as modal order rises. The LDV scan provides that view directly: brightness reveals vibration amplitude, color reveals instantaneous phase, and the transition lines between phase regions identify the shell’s nodal structure. For measurement principles, see Doppler-based laser vibrometry.
Find the antinodes first
Bright regions mark where the dome moves most strongly. Dark bands show nodes or low-response zones. As frequency rises, the response breaks into smaller, more localized lobes around the shell.
Separate in-phase and anti-phase sectors
Opposite colors move in opposite directions. When the map flips from one color family to the other, the shell crosses a nodal line. That makes the circumferential order of each mode visible at a glance.
Track nodal order across the modal series
The aluminum dome progresses from a low-frequency support-influenced response to clearly resolved circumferential shell modes. The increasing nodal complexity helps separate real shell behavior from isolated response peaks.
Non-contact scanning of the dome with a reference-based FRF workflow
The test article was an aluminum hemispherical dome. The visible surface was scanned without contact while a control reference channel supported frequency-response processing and coherence screening. Results below the 0.71 coherence threshold were excluded from interpretation.
- Technique: Scanning Laser Doppler Vibrometer for non-contact full-field surface velocity.
- Reference processing: Frequency-response function versus the EHSC control channel, with coherence screening before interpretation.
- Scan geometry: Phi range from -6.0 degrees to +6.5 degrees in 0.05 degree increments for 251 measurement frames.
- Outputs: Magnitude in dB and phase in radians from -pi to +pi at each resonance peak.
Six resonances reveal a clean circumferential bending series
Read left to right, the measured resonances move from a low-frequency support-influenced response into progressively finer circumferential shell patterns. The 60 Hz response is the first clearly resolved structural mode in this sequence and is best interpreted as a four-lobe circumferential shape. The later 190 Hz and 630 Hz maps follow the same trend with about six and ten lobes, respectively, while the highest-frequency maps show still finer rim scalloping.
Shell theory explains the ordering; the frequency fit checks the scale
Thin-shell vibration theory for spherical and hemispherical shells organizes the response by circumferential order. Higher-order families add more nodal diameters around the shell and therefore appear as finer lobing in the measured maps. The scan follows that ordering: the first structural comparison is the 60 Hz four-lobe response, followed by higher-order patterns near 190 Hz and 630 Hz. For background, see NASA’s Vibration of Shells and the Georgia Tech / NASA report on hemispherical shell response and eigenfunctions.
The frequency check used the measured outer diameter of 278 mm, a nominal shell thickness of 0.70 mm, and generic aluminum properties of E = 69 GPa, density = 2730 kg/m3, and Poisson’s ratio = 0.33. Under those assumptions, the reduced-order model predicts the six resonances at 22.5, 63.5, 196.9, 397.6, 665.4, and 1000.1 Hz. Holding the material fixed and fitting only an effective thickness gives 0.654 mm, aligning the sequence to 21.0, 59.3, 183.9, 371.4, 621.7, and 933.4 Hz.
| Measured mode | Measured | Nominal model, 0.70 mm | Fitted thickness, 0.654 mm | Fit error |
|---|---|---|---|---|
| 1 | 20 Hz | 22.5 Hz | 21.0 Hz | +5.1% |
| 2 | 60 Hz | 63.5 Hz | 59.3 Hz | -1.1% |
| 3 | 190 Hz | 196.9 Hz | 183.9 Hz | -3.2% |
| 4 | 380 Hz | 397.6 Hz | 371.4 Hz | -2.3% |
| 5 | 630 Hz | 665.4 Hz | 621.7 Hz | -1.3% |
| 6 | 925 Hz | 1000.1 Hz | 933.4 Hz | +0.9% |
For engineering use, the fitted thickness acts as an effective scale parameter. It captures tolerance, support compliance and local damping effects while keeping the aluminum material assumption fixed, bringing the modeled frequency sequence within 5.1% of the measured resonances.
From modal testing to industrial vibration mapping
The same non-contact workflow scales from small shell structures to larger industrial assets. For a complete modal workflow, see full-field quantitative modal analysis. For dense vector reconstruction, see 3D velocity field and strain analysis. For field diagnostics on rotating and electrical assets, see the WEG motor and transformer diagnostics example. For system-level context, see Parallel Beam Laser RADAR benefits and the Q2 Laser RADAR. For manufacturer context, see WEG.
Want to turn shell vibration into a usable modal workflow?
Bring the part geometry, expected frequency band, excitation constraints and access limits to define a scan plan, reference strategy and modal dataset that fits the test objective.
