CIVL6264 Chap.9 Vibration, Dynamics and Earthquake Response
Vibration, Dynamics and Earthquake Response
Dynamic performance depends on a mode, a forcing source and a response measure. This chapter distinguishes static deflection, natural frequency, damping and acceleration, then uses a response curve to show how stiffness, mass and damping change different aspects of behaviour.
It extends the load-path method to earthquake action, where diaphragm transfer, cyclic ductility, connection detailing and system regularity determine whether local member capacity can be used. A mode shape states which parts of the structure move together, while natural frequency gives the oscillation rate of that mode.
Modal mass and stiffness locate the frequency, damping controls energy decay and forcing determines whether significant response is excited. Static deflection can indicate flexibility but does not establish acceleration or comfort.
A useful assessment identifies the occupancy and its forcing spectrum, checks plausible modes, calculates the response measure required by the selected criterion and tests whether the proposed remedy targets the controlling component. More stiffness usually raises frequency, more mass tends to lower it and more damping reduces the resonant peak, although real changes can affect several parameters at once.
Earthquake analysis extends the same system discipline to inertia force. Floor mass must pass through the diaphragm and collectors into frames or walls and foundations. Composite columns and joints can contribute ductility only when cyclic details control local buckling and avoid brittle connection failure.
Irregular stiffness and discontinuities can concentrate demand, so a strong member cannot compensate for a broken global path.
What this chapter covers
- 01
Natural frequency and mode shape
- 02
Modal stiffness and mass
- 03
Damping and resonance
- 04
Occupancy forcing
- 05
Diaphragm and collector paths
- 06
Cyclic ductility and earthquake response
Worked example · free
Estimate a frequency change
- +1Cancel the unchanged modal mass.
- +1Write the stiffness ratio as 1.44.
- +1Take the square root to obtain 1.20.
- +1Multiply 7.5 by 1.20 to obtain 9.0 Hz.
- +1State that comfort still needs forcing, damping and response checks.
Key terms
- Natural frequency
- The oscillation rate associated with a free-vibration mode.
- Mode shape
- The relative deformation pattern of a vibrating structure.
- Modal mass
- The portion of system mass participating in a particular mode.
- Damping
- Energy dissipation that limits or decays vibration response.
- Diaphragm
- A floor or roof system transferring in-plane lateral actions to resisting elements.
Vibration, Dynamics and Earthquake Response FAQ
Why is natural frequency not a comfort verdict?
Comfort response also depends on the forcing spectrum, modal mass, damping, mode shape and the acceleration criterion for the occupancy. Two floors with the same frequency can respond differently, and a floor can avoid one harmonic while remaining sensitive to another.
How do stiffness and mass affect frequency?
Natural frequency varies approximately with the square root of stiffness divided by mass for a simple mode. More stiffness tends to raise frequency, while more mass tends to lower it. A real change may affect both, so the net result must be calculated.
Why does earthquake design need a complete load path?
Floor inertia must pass through diaphragms and collectors into frames or walls and then foundations. A strong column cannot help if the diaphragm connection is missing. Cyclic ductility also requires details that avoid brittle local failure under repeated force reversal.
Exam move
For every vibration problem, state the mode, forcing source, modal mass, stiffness, damping and response measure. Recompute the square-root stiffness example and predict the direction before calculating. For earthquake review, draw the diaphragm, collectors, lateral elements and foundations, then mark where cyclic ductility is expected and where brittle failure must be prevented.
For each dynamic problem, write six headings: mode, mass, stiffness, damping, forcing and response criterion. Sketch at least two plausible mode shapes and keep the label beside each computed frequency. Change stiffness or mass and predict the frequency direction before using the square-root relation. If test data are available, compare both frequency and measured shape under documented boundary and occupancy conditions.
For earthquake revision, draw the diaphragm, collectors, lateral frames or walls and foundations, then mark the intended ductile zones and brittle modes to prevent. Review one floor-mass change twice: once for vibration and once for seismic inertia. This exposes why a modification can improve one response while increasing another demand.
Build intuition by changing one parameter in the frequency relation while holding the other fixed, then explain why a real floor modification rarely changes only one parameter. Use a response curve to distinguish moving the natural frequency from lowering a resonant peak. For a measured test, record sensor placement and identify the mode shape rather than reporting one frequency.
Then redraw the same floor as a diaphragm in an earthquake load path. Mark collectors, frames or walls and foundations. This paired exercise shows how floor stiffness and mass influence both occupant response and lateral inertia through different criteria. Close each dynamic review with a measurable acceptance statement.
Name the mode or response to be checked, the occupancy or loading condition and the test or calculation that will confirm performance after construction.