Floor Vibrations — Human Activity Resonance Check

Floor Vibrations — How Resonance Happens and What to Do About It

Floors can feel “bouncy” or even alarming when the frequency at which people or machines excite the structure aligns with the floor’s natural frequency. This is resonance: energy piles up when the input keeps arriving in step with the system’s preferred motion. Human-induced vibration is usually a serviceability issue rather than a strength issue, but comfort and sensitive equipment can be affected well before anything is structurally unsafe.

Key Concepts (in simple terms)

• Natural frequency. Every floor has one (or many). For a 1-m wide strip of a joist floor, a handy model is \(f_1=\dfrac{\pi}{2}\sqrt{\dfrac{EI'}{m' L^4}}\), where \(EI'=\dfrac{E I}{s}\) is flexural stiffness per metre of width, \(m'\) is mass per metre (surface mass \(\mu\)), and \(L\) is the joist span.
• Excitation. People walking, running, or dancing apply periodic forces with dominant frequencies and harmonics. Machines do the same, tied to their rotation speed (RPM) and blade/gear counts.
• Damping. The internal “friction” that bleeds energy away. A modest damping ratio \(\zeta\) (e.g., 2–5%) can drastically reduce peak response at resonance.

Typical Excitation Bands

Walking usually falls around 1.6–2.4 Hz, running 2.3–3.5 Hz, and group fitness/dance can span 2–7 Hz depending on choreography. Because footfall forces are periodic, harmonics at \(2f, 3f, 4f\) matter too: a floor with \(f_1\approx 4.8\) Hz can still resonate with walking if the 2× harmonic sits near that value.

Why some floors feel fine and others don’t

• Stiffness vs. mass. Increasing \(EI'\) (deeper joists, stiffer materials, closer spacing) raises \(f_1\). Adding mass (heavier decking, toppings) lowers \(f_1\). Both can be good or bad depending on the target: you want to avoid the likely excitation band.
• Span length. Frequency scales roughly with \(1/L^2\) for beams (note the \(L^4\) inside the square root). Small increases in span can noticeably drop \(f_1\).
• Continuity and boundary conditions. Real floors aren’t perfect simple beams. Composite action, continuity over supports, and diaphragm behavior can shift frequencies upward.
• Damping and connections. Screws, adhesives, resilient layers, ceiling hangers, and partitions add damping or alter mass/stiffness distribution.

Mitigation Playbook

• Detune the structure. Raise \(f_1\) (add stiffness, reduce span, add secondary beams) or lower it (add mass) so that \(f_1\) and key harmonics miss the excitation range by a comfortable margin.
• Add damping. Resilient underlays, viscoelastic layers, tuned mass dampers (TMDs), and improved connections can cut peak response near resonance without large geometric changes.
• Control the source. Shift machine RPM, balance rotating parts, decouple with isolators, or relocate activities away from response “hot spots” (antinode regions near mid-span for the first mode).

What this tool’s model assumes

The joist model treats a 1-m wide strip as a simply supported beam with a lumped surface mass \(\mu\). That’s great for screening and comparisons but not a substitute for a full finite-element model or a code-based design check. Irregular framing, openings, composite decks, and heavy non-structural items can shift the real frequency.

Practical checks

• Compare harmonics. Always check \(f, 2f, 3f, 4f\) against your floor’s \(f_1\).
• Look at deflection, too. A quick mid-span deflection estimate under a 1 kN test load is a useful sanity check for stiffness and perceived “bounce.”
• Measure if in doubt. A smartphone accelerometer app can capture a dominant frequency during a short walk test. If it clusters near your computed \(f_1\), you’re on the right track.

The goal isn’t zero vibration; it’s avoiding uncomfortable resonance and keeping sensitive uses happy. Use this tool to explore “what-ifs,” then refine with detailed analysis or a structural engineer when the stakes are high.