Vibration Transmissibility Calculator
Ideal single degree displacement/force transmissibility at frequency ratio r=ω/ωn, actual dampingζ; no base isolation safety or multidof response. Actual independently established compatible SI units/model context; conditional arithmetic, not code compliance, engineering design or safe operation approval.
Description
An ideal single-degree-of-freedom transmissibility depends on damping and excitation-to-natural-frequency ratio.
An ideal single-degree-of-freedom transmissibility depends on damping and excitation-to-natural-frequency ratio.1
This tool evaluates the supplied linear model without solving a multidimensional system or assessing isolation safety.
When to use Vibration Transmissibility Calculator
Use this tool to evaluate the supplied linear model without solving a multidimensional system or assessing isolation safety.
How to use Vibration Transmissibility Calculator and how it works
- Prepare dampingRatio, frequencyRatio, with the units, conventions and assumptions below.
- Enter the required fields and run Vibration Transmissibility Calculator.
- Read result.value using the output definitions below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| dampingRatio | Dimensionless damping ratio zeta on the tool-specific branch below. | number | Required; nonnegative; finite; other constraints below |
| frequencyRatio | Nonnegative excitation frequency divided by natural frequency, using matching frequency units. | number | Required; nonnegative; finite; other constraints below |
Supply nonnegative damping ratio zeta and nonnegative excitation-to-natural-frequency ratio r. Calculate sqrt((1+(2*zeta*r)^2)/((1-r^2)^2+(2*zeta*r)^2)) and require a positive denominator. Undamped resonance at r=1 is rejected rather than assigned an infinite transmissibility.
transmissibility=sqrt((1+(2*zeta*r)^2)/((1-r^2)^2+(2*zeta*r)^2)) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Dimensionless single-degree-of-freedom transmissibility magnitude. | number |
{
"input": {
"dampingRatio": 0.5,
"frequencyRatio": 0
},
"output": {
"result": {
"value": 1
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Step Response Overshoot Calculator for a complementary operation: Ideal underdamped second-order step overshoot depends on damping ratio within a restricted branch.
Use Settling Time Calculator for a complementary operation: A specified exponential envelope reaches a chosen fraction according to its decay rate.
References
-
Vibration Transmissibility Calculator — tool.io
Similar or alternative tools
- Step Response Overshoot Calculator
Ideal underdamped second-order step overshoot depends on damping ratio within a restricted branch.
- Settling Time Calculator
A specified exponential envelope reaches a chosen fraction according to its decay rate.