Vibration analysis
Skid vibration isolation
A vertical and pitch isolation study for a rotating-equipment skid. It compares support stiffness and damping, startup resonance, foundation motion and load variation.
Coupled dynamics study with executed uncertainty and transient checks

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
Skid force transmission
Compare the included analysis results.
| Candidate support combinations | 30 |
|---|---|
| Selected base pair stiffness | 120.0 kN/m |
| Selected damping parameter | 0.1 |
| Worst running-band foot-force envelope | 7.5769 N |
| Worst combined relative-motion bound | 1.26483 mm |
| Maximum combined support-pair load | 923.6 N |
| Executed uncertainty corners | 32 |
Report figures (5)




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.pyDownload the verification record ↓Additional scenarios
19 outcomes checked through executed numerical and synthetic dynamics study. The report lists the expected and observed outcomes for each check.
Read the validation report ↗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
Archive checksum
SHA-256
aae263b9df3e4037438cec009a26b5b7d2f0286134963e01a3b3266be61d969fRun 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.pyLimits
- 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.