Shaking that repeats: rotating machinery, earthquakes, transport — and the accumulated damage from millions of cycles.
1. What is it?
Frequency response: shake the base at every frequency 0→N Hz; get the amplification curve. "At motor speed this panel moves 6× the input."
Response spectrum (SRSS): an earthquake/ship/shock spec gives you a spectrum, not a time history. Get peak response per mode, combine with SRSS. "Code says this shelf must survive the design spectrum."
Random vibration (PSD): the input is statistical (power spectral density). Get RMS response. "This electronics box must survive the launch vehicle random vibration spec."
Fatigue life: under repeated loading, cracks initiate and grow. "This shaft rotates 10⁷ cycles — will it survive?"
2. When do I use which?
You have…
Use
Example
Frequency sweep input
Frequency response
Find resonance peaks
Shock/earthquake spec
Response spectrum
Code compliance
Random vibration spec (PSD)
Random vibration
Aerospace qualification
Repeated loading
Fatigue life
Rotating machinery
Use cases
Problem Type
Industry
Example
Component life prediction
Automotive
Control arm fatigue life
Weld fatigue
Offshore
Tubular joint S-N analysis
Thermal fatigue
Power plants
Thermal sleeve cracking
Random vibration fatigue
Aerospace
Electronics board resonance fatigue
Motor critical speed
Energy/Turbine
Rotor resonance avoidance
Earthquake code compliance
Civil/Structural
Building response spectrum
3. The flow
Frequency Response
Design — geometry
Boundary — material + supports + base excitation
Mesh — generate
Simulate → Frequency Response → set frequency range
Results — amplification vs frequency
Response Spectrum
Design — geometry
Boundary — material + supports + spectrum definition
Mesh — generate
Simulate → Response Spectrum → select spec
Results — peak response per mode, SRSS combination
Random Vibration
Design — geometry
Boundary — material + supports + PSD input
Mesh — generate
Simulate → Random Vibration → set frequency range
Results — RMS stress, 3-sigma peaks
Fatigue Life
Design — geometry
Boundary — material (S-N curve) + cyclic load
Mesh — generate
Simulate → Fatigue → set cycle count
Results — damage ratio, predicted life
4. Reading your results
Frequency Response
Result
Meaning
Peak amplification
Maximum response / input at resonance
Resonance frequency
Frequency at which peak occurs
Bandwidth
Range of high amplification
Good: Operating frequency avoids resonance peaks. Bad: Operating frequency coincides with resonance.
Response Spectrum
Result
Meaning
Peak displacement
Maximum response to the spec
Peak stress
Maximum stress during the event
SRSS combination
Root-sum-square of modal responses
Random Vibration
Result
Meaning
RMS stress
Statistical average stress
3-sigma peak
Stress exceeded 0.3% of the time
PSD response
Output power spectral density
Fatigue Life
Result
Meaning
Damage ratio
Fraction of life consumed per cycle
Predicted cycles
Number of cycles to failure
Safety factor
Ratio of allowed to applied cycles
Good: Predicted life > required life × safety factor. Bad: Damage ratio > 1 → failure expected.
5. Boundaries of truth
What's validated
Case
Reference
Error
Frequency response
Analytical
< 2%
Response spectrum
Published
< 3%
Random vibration (PSD)
Published
< 5%
Fatigue (S-N)
Published
< 10%
What's NOT covered
Multiaxial fatigue — single-axis only
Weld fatigue — plain material only
Wide-band random — narrow-band assumptions
Crack growth — initiation only, not propagation
Common mistakes
Mistake
Fix
Missing damping
Add damping ratio (typically 0.01-0.05)
Too few modes
Include modes up to 2× highest frequency
Wrong S-N curve
Use material-specific data
Ignoring mean stress
Apply Goodman/Gerber correction
See also
[Dynamics](dynamics.md) — for time-domain analysis
[Static Structural](static-structural.md) — for static strength