The exact same force amplitude, applied at different frequencies, can produce a response 20 times larger — not because the force changed, but because of how close its frequency lands to the structure's own natural frequency.
Structural dynamics analyzes how structures respond to time-varying loads — wind gusts, earthquakes, machinery vibration, foot traffic — rather than static loads. Every structure has one or more natural frequencies, the frequencies at which it 'wants' to vibrate on its own, and how close an applied dynamic load's frequency comes to that natural frequency dramatically changes how large the structural response becomes, a phenomenon called resonance.
For a dynamic (time-varying) load, the resulting structural response depends not just on the force's magnitude but critically on its frequency relative to the structure's natural frequency, captured by the dynamic amplification factor. As shown above, that amplification factor peaks sharply near a frequency ratio of 1 (forcing frequency equals natural frequency) — this is resonance, and it means the same force amplitude can produce a response many times larger than the same force applied slowly (statically) or far from resonance.
In theory, an undamped system at exact resonance would see amplification grow without bound. Real structures always have some damping (energy dissipation from material friction, structural connections, or added damping devices), which caps the resonant peak at a finite — though often still very large — amplification factor, as reflected in the amplification formula's dependence on the damping ratio.
Structural and mechanical designers work specifically to keep a structure's or machine's natural frequency well away from the frequency of any significant expected dynamic load — a building's natural frequency versus expected wind-gust or seismic frequency content, a rotating machine's operating speed versus its supporting structure's natural frequency, a footbridge's natural frequency versus typical pedestrian walking frequency. Getting this wrong has caused real, well-documented structural failures and serviceability problems historically, which is exactly why resonance avoidance is standard practice, not an afterthought.
A structure's natural frequency is the frequency at which it will vibrate on its own if disturbed and then left alone (like a plucked guitar string) — it's determined entirely by the structure's own mass and stiffness distribution, independent of any external applied load.
No — any dynamic load source can cause resonance if its frequency content overlaps with a structure's natural frequency: wind-induced vortex shedding, rotating machinery vibration, pedestrian or vehicle-induced vibration on bridges, and seismic ground motion are all real, distinct sources of dynamic loading that structural dynamics analysis must consider.
Away from resonance, the response is dominated by the difference between forcing and natural frequency, and damping has only a modest effect on the result. Right at resonance, that frequency-difference term vanishes entirely, leaving damping as essentially the only thing limiting how large the response grows — which is exactly why the amplification curve's peak height is so sensitive to the damping ratio specifically near a frequency ratio of 1.
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