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Assessing Vibration Resistance

A90·Nov 8, 2026·Source: Web

Assessing Vibration Resistance of Metal Structures

Quick Start15 / 15

Given a structure and an external vibration source, determine resonance risk in 4 numbers:

Source frequency f_source (Hz) — from equipment specs, measured accelerometer data, or standard tables (e.g., fans 16.7–50 Hz, piston compressors 4–25 Hz, pedestrian bridges 1.6–2.4 Hz, seismic 0.1–10 Hz).
Structure's natural frequency f_n — from modal analysis (FEM) or simplified formula:
```
f_n = (1 / 2π) * sqrt(k / m)
```
where k = structural stiffness (N/m), m = effective mass (kg).
Frequency ratio β = f_source / f_n.
Dynamic amplification factor (DAF):
```
DAF = 1 / sqrt((1 - β²)² + (2ζβ)²)
```
where ζ = damping ratio (steel welded: 0.01–0.02; bolted: 0.02–0.04; with dampers: 0.05+).

Rule of thumb: if 0.8 < β < 1.25 → resonance zone, redesign required. If DAF > 1.5 → reinforce or add damping.

Recommendation▾

Add a third example covering seismic or wind-induced vibration to broaden scenario coverage beyond machinery sources

Workflow14 / 15

Progress:

Step 1: Characterize the vibration source
Step 2: Determine structural dynamic properties
Step 3: Compute frequency ratio and DAF
Step 4: Compare against resonance and fatigue limits
Step 5: Recommend mitigation if needed
Step 6: Document and verify (measurement or re-analysis)

Step 1: Characterize the Source

Identify type: rotating machinery, impact/periodic, seismic, wind/vortex shedding, traffic.
Get: frequency range (Hz), amplitude (mm or g), force magnitude (N), duty cycle (continuous/transient).
If unmeasured, use manufacturer data or codes (ISO 10816 for machine vibration severity, GOST/SNiP seismic tables, EN 1991-1-4 for wind).

Step 2: Structural Dynamic Properties

Build simplified lumped-mass model or full FEM (SAP2000, ANSYS, SCAD, Lira).
Extract first 3–5 natural frequencies and corresponding mode shapes.
Estimate damping ratio ζ based on connection type and material.
For simple beams/frames, use analytical formulas (Euler-Bernoulli beam, Dunkerley's method) as a sanity check against FEM.

Step 3: Compute β and DAF

Compute β for each relevant mode vs. each source frequency component (include harmonics 2f, 3f for rotating machinery).
Compute DAF per mode.
Flag any mode where β falls in [0.8, 1.25].

Step 4: Compare Against Limits

Resonance check: DAF threshold per application (machinery foundations: DAF < 1.5 typical; precision equipment: stricter, DAF < 1.2).
Fatigue check: estimate stress cycles using Miner's rule if long-term cyclic loading; compare to S-N curve of material/welds (EN 1993-1-9).
Serviceability check: compare peak displacement/velocity/acceleration to comfort or equipment-sensitivity limits (ISO 2631 for human perception, ISO 10816 for machinery).

Step 5: Mitigation (if limits exceeded)

Ordered by typical cost-effectiveness:

Detune — add/remove mass or stiffness to shift f_n away from f_source (target β < 0.7 or β > 1.4).
Increase damping — tuned mass dampers, viscoelastic layers, friction dampers.
Isolate — vibration isolators/springs between source and structure (isolation effective when f_source / f_n_isolator > √2).
Stiffen/reinforce locally at high-stress nodes identified by mode shapes.
Relocate or reorient source relative to structure if feasible.

Step 6: Document and Verify

Report: source data, model assumptions, computed β/DAF per mode, pass/fail, recommended mitigation.
If critical, validate with field measurement (accelerometers) post-construction or post-retrofit.

Recommendation▾

Include a brief note on units/sanity-check ranges for typical k and m values to help estimate f_n when FEM is unavailable

Examples18 / 20

Example 1: Input: Steel platform supporting a fan rated at 1450 rpm (24.2 Hz). FEM gives f_n1 = 23.8 Hz, ζ = 0.015 (welded steel). Output: β = 24.2/23.8 = 1.017 → resonance zone. DAF = 1/√((1−1.017²)² + (2·0.015·1.017)²) ≈ 1/√(0.00117 + 0.00093) ≈ 21.7 → severe resonance. Recommendation: add stiffening ribs to raise f_n1 to ≥30 Hz (β ≈ 0.81, DAF ≈ 2.8) or add tuned mass damper; preferred: increase stiffness since mass addition alone insufficient. Re-run modal analysis after change.

Example 2: Input: Pipe rack near a reciprocating compressor, fundamental excitation 8.3 Hz (2nd harmonic 16.6 Hz). Structure f_n = 15.9 Hz, ζ = 0.02. Output: Check fundamental: β1 = 8.3/15.9 = 0.52 → safe, DAF ≈ 1.37. Check 2nd harmonic: β2 = 16.6/15.9 = 1.044 → resonance risk, DAF ≈ 12.1 (critical). Recommendation: shift f_n away from 16.6 Hz by adding bracing (target f_n > 20 Hz) or install compressor on isolated foundation with f_isolator < 11 Hz (isolation ratio √2 margin against 16.6 Hz).

Recommendation▾

Add a short troubleshooting section for when measured field data contradicts FEM predictions

Best Practices

Always check multiple modes, not just the fundamental — higher modes can coincide with harmonics.
Include harmonics (2×, 3× rotational speed) for rotating equipment, not just fundamental frequency.
Use conservative (lower-bound) damping values unless measured — underestimating ζ overestimates DAF, which is safe-sided.
Cross-check FEM natural frequencies with a simplified hand calculation; large discrepancies indicate modeling errors.
For seismic sources, use response spectrum analysis rather than single-frequency DAF, since excitation is broadband.
Reassess after any structural modification (added equipment, cut openings, corrosion loss) — mass/stiffness changes shift f_n.

Common Pitfalls

Ignoring harmonics of the source frequency — fundamental may be safe while 2nd/3rd harmonic hits resonance.
Using static stiffness in k without accounting for connection flexibility (bolted joints behave less stiff dynamically than assumed).
Assuming damping ratio of 0.05 (typical for concrete) for welded steel structures — leads to dangerously optimistic DAF.
Treating isolation and detuning as interchangeable — isolators require f_source >> f_n_isolator; adding stiffness to "detune" can accidentally move f_n toward the source frequency instead of away.
Neglecting soil-structure interaction for ground-mounted equipment — foundation flexibility can lower effective f_n significantly.
Performing only a static analysis and skipping modal/dynamic analysis entirely when the source is clearly periodic.