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Virtual Shake Table

Choose a shake table, build a specimen, shake it with an NBC 105 earthquake, a sine sweep or shock pulses, and see how it responds. Every run checks the table’s limits and produces a full test report.

The principle

Shake the base, let inertia do the rest.

A shake table moves the base of a structure the way the ground moves in an earthquake. Nothing pushes the floors: the seismic forces come from the structure’s own mass resisting the acceleration, m ü + c u̇ + k u = −m üg.

  1. Shake tablePick one of eight table types, from a bench-top teaching unit to a 20 m × 15 m 3-D table, or enter your own limits.
  2. Specimen & motionShear building up to 20 storeys, with isolation, a TMD or yielding storeys. Eight motion types or your own record.
  3. Run & reportScale the model, check stroke, velocity, acceleration and payload, watch the test, then download the PDF report.
Theory behind the simulator

How the numbers are made.

Standard structural dynamics, the methods used to prepare real shake table tests, and NBC 105 for the target earthquake.

Equation of motion on a moving base

For a multi-storey building the same idea holds with matrices. Forces are spread over the height where the mass actually is, so no lateral load pattern has to be assumed.

M ü + C u̇ + Fs(u) = − M ι üg(t)

The building is a lumped-mass shear building. Storey stiffness is scaled so the fixed-base period equals your T₁, and damping is Rayleigh damping fitted to ξ in the first two modes.

Modes and effective mass

(K − ω²M) φ = 0 · Γ = φᵀMι / φᵀMφ

Natural periods and mode shapes come from the eigenvalue problem. The effective modal mass shows how much of the building each mode moves; the first mode usually carries 80–90 % of a regular building.

Resonance and transmissibility

TR = √[(1 + (2ξr)²) / ((1 − r²)² + (2ξr)²)]

When the table frequency is close to the structure’s own frequency (r = ω/ωₙ ≈ 1), the top accelerates many times more than the table. That is why tests start with a sine sweep or white noise to find ωₙ.

Time integration and yielding

The response is computed step by step with explicit central-difference integration, using a time step well below the stability limit. Yielding storeys and lead-rubber bearings follow a bilinear hysteresis rule, so you can see the base shear–drift loops and the energy they dissipate.

Preparing the ground motion

A tiny offset in an accelerogram turns into metres of drift after double integration. Records are tapered, high-pass filtered and baseline-corrected so velocity and displacement end at zero, then scaled. If the stroke is still too small, time can be compressed while keeping peak acceleration, the approach Quanser describes for small tables.

NBC 105 spectrum-compatible records

C(T) = Ch(T) · Z · I

Artificial records are built from random-phase sinusoids under a strong-motion envelope and adjusted until their 5 % damped response spectrum matches the NBC 105 elastic site spectrum for the chosen soil type, zone factor and importance class.

Scale models and similitude

Gravity cannot be scaled on a shake table, so reduced-scale models follow a similitude law. With artificial mass simulation (same material, added mass): time ÷ √λ, frequency × √λ, acceleration unchanged, displacement ÷ λ, force and mass ÷ λ². The simulator uses these factors to check the scaled test against the table’s limits.

Isolation and tuned mass dampers

kb = M(2π/Tb)² · fd/f₁ = 1/(1+μ) · ξd = √[3μ/8(1+μ)³]

Base isolation lengthens the period beyond the strong part of the spectrum; a tuned mass damper is tuned with Den Hartog’s rules. Each protected run is compared with the same building on a fixed base.

References

  1. Chopra, A.K. Dynamics of Structures, Pearson.
  2. Severn, Stoten & Tagawa (2012), The contribution of shaking tables to earthquake engineering, 15WCEE.
  3. Harris & Sabnis (1999), Structural Modeling and Experimental Techniques.
  4. Nigam & Jennings (1969), response spectra from strong-motion records, BSSA.
  5. NBC 105:2025, Seismic Design of Buildings in Nepal.
  6. Facility and manufacturer data: E-Defense, EUCENTRE, CSIR-SERC, MTS, QuakeLogic, Quanser, NSET, IOE Pulchowk.
  7. Inspired by the open Virtual Shake Table by Claudio Sepúlveda.