Skid vibration isolation

Implementation

A two-degree-of-freedom rigid-body model couples vertical translation and pitch through asymmetric support pairs.

Complex frequency-response calculations compare a finite grid of 30 support choices over 32 parameter corners.

A smooth angular-frequency schedule is integrated analytically; its radial and angular-acceleration forces drive the transient ODE.

The selected design is integrated through startup, hold, stop and a foundation pulse at every uncertainty corner. Conservative peak sums cover arbitrary timing of the two disturbances.

Implicit stiffness derivatives, energy/work integrals and scalar/steady-state limits provide independent checks of the numerical model.

Inputs and assumptions

• 120 kg reference skid with 18 kg m² pitch inertia, support positions -0.42 m and +0.36 m, and 0.002 kg m rotating unbalance.
• Each support group represents a pair of linear spring/viscous-damper mounts sharing left/right load equally.
• The operating band is 20-35 Hz. Mass varies ±10%, CG shifts ±0.04 m, each support stiffness varies ±10%, and common damping varies ±20%.
• A 1 mm, 0.15 s foundation pulse is a synthetic design input. Pitch inertia scales with mass and is defined about the shifted CG.

Results

Report figures (5)

Open the full report ↗

Verification

22 regression tests, 12 independent numerical checks and 19 acceptance checks pass. All 32 selected-design corners satisfy the declared operating and combined transient limits; the stiff retrofit is rejected for force transmission.

python run.py

Project files

The ZIP contains the source, inputs, results, and instructions. These files are also available individually.

• Coupled dynamics model and calculusmodel.py · 8 KB
• Candidate and uncertainty evaluationstudy.py · 8 KB
• Reference design inputsinputs.json · 1 KB
• Frequency-response resultsoutputs/frequency-response.csv · 74 KB
• Candidate search and rejectionsoutputs/candidate-grid.csv · 5 KB
• All selected-design corner outcomesoutputs/uncertainty-corners.csv · 9 KB
• Start/stop and energy traceoutputs/runup.csv · 824 KB
• Foundation-pulse traceoutputs/foundation-pulse.csv · 335 KB
• Coordinates and support schematicoutputs/model.svg · 2 KB
• Technical report and derivationsreport.html · 15 KB
• Independent numerical verificationvalidation.py · 5 KB
• Executed regression logoutputs/test-results.txt · 2 KB
• Executed acceptance auditcompletion/report.html · 5 KB
• Acceptance outcomes and source hashescompletion.json · 7 KB

Run locally

Python 3.11+ / NumPy 2.3.5 / SciPy 1.17.0 / Matplotlib 3.10.8

Extract the ZIP and open a terminal in the skid-vibration-isolation folder. The README includes setup and usage details.

python -m pip install -r requirements.txt
python run.py
python complete_validation.py
python -m unittest -v test_project.py

Limits

• The body is rigid with vertical and pitch motion only. Roll, lateral motion, frame flexibility, piping loads and floor flexibility are outside this model.
• Equivalent support stiffness and viscous damping are declared assumptions. No commercial mount properties, temperature dependence, creep or nonlinear contact were measured.
• The finite candidate/corner search is not a global optimum, a probability of success or a proof over every interior uncertain point.
• The transient peak bound includes 1% allowance, checked at nominal and limiting corners with finer output sampling. The pole-based decay indicator is not a universal initial-condition settling guarantee.
• This completes a numerical reference study and synthetic commissioning scenarios. No physical fabrication, fatigue qualification or field measurement is claimed.