Analysis & loading · Seismic & dynamic
Machine foundation (vertical mode) calculator
Vertical stiffness and damping of a rigid circular base, natural frequency and frequency ratio against the operating speed.
Standard: Lysmer analog (elastic half-space)
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Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Machine + block mass | 60 | t |
| Equivalent base radius | 2 | m |
| Soil shear modulus | 60 | MPa |
| Poisson's ratio | 0.33 | |
| Soil density | 1.9 | t/m³ |
| Operating speed | 600 | rpm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| kz = 4 G r0/(1 − ν) | 716,418 | kN/m |
| Mass ratio Bz = (1 − ν)m/(4ρr0³) | 0.661 | |
| Damping ratio 0.425/√Bz | 0.523 | |
| fn = (1/2π)√(kz/m) | 17.39 | Hz |
| Operating frequency | 10.00 | Hz |
| Frequency ratio fo/fn | 0.575 |
- ✓ Avoid resonance: ratio outside 0.8–1.25
Method, formulas and assumptions
- kz = 4 G r0/(1 − ν) = 4*60*1000*2/(1-0.33) = 7.164e+5 kN/m
- Mass ratio Bz = (1 − ν)m/(4ρr0³) = (1-0.33)*60/(4*1.9*2^3) = 0.66118
- Damping ratio 0.425/√Bz = 0.425/SQRT(0.66118) = 0.52267
- fn = (1/2π)√(kz/m) = SQRT(7.164e+5/60)/(2*PI()) = 17.391 Hz
- Operating frequency = 600/60 = 10 Hz
- Frequency ratio fo/fn = 10/17.391 = 0.57501
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.