Uni-Axial Computer-Controlled Earthquake Shake Table
Linear servo-motor drive table (payload 50 kg, stroke ±75 mm, frequency 0.1 to 20 Hz, peak acceleration 2.0 g).
Civil Engineering / Shake Table Resonance
FREE TO EXPLORELABORATORY 48 · CIVIL ENGINEERING
Harmonic Base Excitation & Dynamic Amplification on a Single-Axis Shake Table
Excite structural model on a computer-controlled uni-axial shake table across variable harmonic frequencies (0.5 to 10 Hz), plot dynamic amplification factor (DAF) response spectrum, and observe structural resonance and phase shift. Explore interactive structural mechanics, materials simulation, and civil engineering telemetry.
STRUCTURAL MATERIALS · MECHANICS · GEOTECHNICAL · HYDRAULICS · HIGHWAYS · SURVEYING
Your virtual civil engineering laboratory.
PEAK ROOF STRUCTURAL ACCELERATION A_ROOF—
CIVIL INFRASTRUCTURE TELEMETRY
Ready to sample with Base Accel a_base = 0.6 m/s².
Adjust Base Accel a_base, then execute civil engineering measurement.
Civil engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity structural mechanics and geotechnical continuum modeling.
Civil engineering assumptions and boundary condition limits
The civil engineering physical models apply within the specified calibrated operational window (0.2 to 1.2 m/s²). Tested on a 1-story steel building model (f_n = 2.80 Hz, ζ = 5.88%) mounted on an electro-mechanical shake table. Linear model correlates peak roof acceleration a_roof directly to base acceleration a_base at resonance with amplification slope DAF = 8.5000.
Laboratory apparatus & testing equipment.
Single-Story Structural Steel Frame Model
Rigid aluminum top mass (m = 5.0 kg) supported by spring steel column blades (f_n = 2.80 Hz).
Dual Piezoelectric Base & Roof Accelerometers
Low-frequency accelerometers measuring base input a_base and roof response a_roof simultaneously.
Non-Contact Optical Laser Displacement Transducer
Records relative inter-story floor drift u(t) to ±0.01 mm resolution.
Dynamic Digital Controller & Signal Generator
Generates precision sine-dwell, sine-sweep, and scaled historical earthquake ground records (e.g. 1940 El Centro).
High-Speed Video Camera (240 fps)
Visually captures phase angle shift and resonant structural deflection shapes.
FOLLOW THE METHOD
A reason behind every step.
Excite structural model on a computer-controlled uni-axial shake table across variable harmonic frequencies (0.5 to 10 Hz), plot dynamic amplification factor (DAF) response spectrum, and observe structural resonance and phase shift. Standardized parameter settings: 0.2, 0.4, 0.6, 0.8, 1.0, 1.2 m/s².
01
Model Fastening & Shake Table Instrumentation
Bolt base plate of structural frame securely to shake table platen; mount accelerometer on table surface (a_base) and roof mass (a_roof); align laser displacement sensor to roof target.
02
Initial Low-Amplitude Sine-Sweep (0.5 to 10 Hz)
Drive shake table with constant low base acceleration (0.1 m/s²) across a logarithmic sine sweep from 0.5 to 10.0 Hz to identify peak resonant frequency f_n = 2.80 Hz.
03
Resonant Sine-Dwell Base Excitation
Tune signal generator to exact resonance f_res = 2.80 Hz; apply initial base acceleration amplitude a_base = 0.20 m/s²; allow 20 cycles to attain steady-state harmonic motion.
04
Peak Acceleration & DAF Recording
Record steady-state peak base acceleration a_base and peak roof response a_roof; calculate Dynamic Amplification Factor DAF = a_roof / a_base.
05
Systematic Base Acceleration Escalation
Increase base acceleration amplitude across six systematic levels (0.2, 0.4, 0.6, 0.8, 1.0, and 1.2 m/s²); record peak roof accelerations for each run.
06
Phase Angle Shift Verification & Response Spectrum Plotting
Observe phase delay between base and roof signals on digital oscilloscope; verify 90° phase shift at resonance; plot a_roof versus a_base to determine empirical DAF.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into civil engineering insight.
Points are your recorded observations. The solid regression line validates Shake Table Resonance mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
a_roof = 8.5000 · a_base
| # | Peak Base Ground Acceleration a_base (m/s²) | Peak Roof Structural Acceleration a_roof (m/s²) | Peak base input acceleration a_base (m/s²) | Resonant peak roof response acceleration a_roof (m/s²) | Remove |
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CHECK YOUR UNDERSTANDING
Explain what the civil engineering metrics mean.
At exact resonance (frequency ratio β = 1.0), the theoretical maximum Dynamic Amplification Factor for viscous damping ζ is:
If a structure has a viscous damping ratio of ζ = 5% (0.05), its maximum resonant amplification factor is:
At exact resonance, the phase angle by which structural response lags harmonic base excitation is:
Seismic base isolation protects buildings primarily by:
THEORY AND STRUCTURAL CONTEXT
Civil engineering background & physical principles.
During severe earthquake events, seismic ground motions transmit harmonic and transient shock waves through building foundations, inducing base excitations that travel upward into the superstructure. When external ground shaking frequency ω matches the building's fundamental natural frequency ω_n (frequency ratio β = ω / ω_n ≈ 1.0), the structure enters catastrophic resonance, amplifying roof accelerations and inter-story drifts to many times the ground input. Evaluated on a computer-controlled single-axis earthquake shake table, a structural frame is subjected to harmonic sinusoidal base acceleration: u_g(t) = a_base · sin(ω·t). The steady-state relative displacement response is governed by the Dynamic Amplification Factor (DAF): DAF = 1 / √[(1 - β²)² + (2·ζ·β)²], where ζ is the viscous damping ratio. At exact resonance (β = 1.0), the theoretical amplification factor reaches its maximum value: DAF_max = 1 / (2·ζ). For a typical civil engineering steel frame with damping ratio ζ ≈ 5.88% (0.0588), the peak resonant amplification factor is exactly DAF = 1 / (2 · 0.0588) = 8.5000. In addition, the phase angle between base excitation and structural response shifts from 0° (quasi-static in-phase tracking at low frequencies β << 1), to exactly 90° at resonance (β = 1.0), and finally to 180° (complete out-of-phase motion at high frequencies β >> 1). In this laboratory shake table experiment, base acceleration amplitudes from 0.2 to 1.2 m/s² at resonant frequency (f = 2.80 Hz) are delivered to the model to calibrate the resonant amplification slope = 8.5000, verify the DAF spectrum, and evaluate seismic inertia forces.
a_roof = 8.5000 · a_base
Tested on a 1-story steel building model (f_n = 2.80 Hz, ζ = 5.88%) mounted on an electro-mechanical shake table. Linear model correlates peak roof acceleration a_roof directly to base acceleration a_base at resonance with amplification slope DAF = 8.5000.