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Structural dynamics · transmissibility

How Motion and Force Travel

Track vibration passing through supports and isolation elements.

Approx. 32 min

Learning objectives

By the end of this lesson

  • Define transmissibility in physical engineering terms.
  • Use force transmissibility with consistent quantities and units.
  • Change model inputs and explain the resulting trend.
  • Separate an educational model result from a code-based safety decision.

Before you calculate

What this means in the real world

01

What the formula is for

Isolation begins only in the appropriate frequency-ratio range; added damping has different effects near and far from resonance.

TR = √[(1+(2ζr)²)/((1−r²)²+(2ζr)²)]
02

Where an engineer uses it

Vibration isolation beneath a generator: This application turns transmissibility into a real modelling decision.

Estimate the supported mass and isolator stiffness to place the operating frequency in an isolation region.

03

What a wrong value can do

A wrong unit, sign, scale, boundary condition, or property can produce a believable number with the wrong physical meaning. It may understate demand, exaggerate it, or lead to the wrong failure check.

Definition

transmissibility

A dimensionless ratio comparing transmitted response with the applied force or base motion.

Why it mattersIt provides the central modelling idea for how motion and force travel and connects observed motion to a solvable engineering representation.

Build the physical picture

Track vibration passing through supports and isolation elements. Start by identifying the system boundary, response coordinates, applied action, and the properties that store or dissipate energy. A useful model is the simplest one that preserves the behaviour needed for the engineering question.

Formula

Force transmissibility

TR = √[(1+(2ζr)²)/((1−r²)²+(2ζr)²)]

Isolation begins only in the appropriate frequency-ratio range; added damping has different effects near and far from resonance.

u
response displacement or displacement vectorm
t
times
ω
angular frequency where usedrad/s

Interactive concept

Explore transmissibility

Change the available model inputs, watch the motion or force relationship, and describe the trend before reading the numerical result.

How is the load applied?
How does the structure behave?
LoadTime →
Load⇣
Lower dynamic tendency

A gradual action on a relatively rigid structure is more likely to remain close to static behaviour.

08

Real-world application

Vibration isolation beneath a generator

This application turns transmissibility into a real modelling decision.

Modelling move
Estimate the supported mass and isolator stiffness to place the operating frequency in an isolation region.
Engineering question
Will the selected isolator reduce or amplify transmitted action?

Calculate, compare, interpret

Editable formula question

Experiment with period: How Motion and Force Travel

Change mass and stiffness, predict the period, and check your result.

Tₙ = 2π√(m/k)
Substitute your current valuesTₙ = 2π√(1000 ÷ 40000)Answer format: enter the numerical result only in s. Example: 12, not “answer = 12”.
s
Round only at the final step. The accepted tolerance for this exercise is ±0.01.

The displayed minimum, maximum, and textbook values define this learning exercise only. They are not universal design limits.

Editable formula question

Compare a model demand with your entered criterion

Enter a demand and a comparison value chosen for this exercise, then interpret the ratio.

utilization indicator = model demand / entered criterion
Substitute your current valuesratio = 4 ÷ 5Answer format: enter the numerical result only (no unit for this dimensionless result). Example: 12, not “answer = 12”.
—
Round only at the final step. The accepted tolerance for this exercise is ±0.01.

The displayed minimum, maximum, and textbook values define this learning exercise only. They are not universal design limits.