Glossary term

Transmissibility

Dimensionless dynamic response ratio used to compare transmitted force, motion or acceleration with an applied excitation or base motion.

Branch: Mechanical Engineering
Glossary type: metric
Content: Glossary term
Updated: Jun 25, 2026
Revision: v1.0.1 · reviewed

Definition

metric

Transmissibility is a dimensionless dynamic ratio that compares a transmitted response with an applied input, such as transmitted force divided by excitation force or payload motion divided by base motion.

In vibration engineering, transmissibility describes how much force, displacement, velocity or acceleration passes through a mount, support, structure or isolation system at a given frequency. It is usually a magnitude ratio, often accompanied by phase. Values greater than 1 indicate amplification, while values less than 1 indicate attenuation for the stated input, output, direction, frequency band and boundary condition.

Transmissibility is the ratio between an output response and an input excitation in a dynamic system. It is used when engineers need to know whether a mount, foundation, structure, fixture, payload interface or support path amplifies or attenuates vibration.

The generic ratio is:

\displaystyle T(\omega)=\left|\frac{\text{output response}}{\text{input excitation}}\right|

The ratio is dimensionless when the output and input are the same physical quantity, such as acceleration-to-acceleration or force-to-force. It can also be reported in decibels:

T_{\mathrm{dB}}=20\log_{10}(T)

Transmissibility must always state what is being transmitted. Force transmissibility, absolute motion transmissibility, relative displacement transmissibility and acceleration transmissibility are related, but they are not interchangeable without the model and measurement convention.

Engineering Role

Transmissibility is central to vibration isolation, base-excitation response, rotating-machinery support design, equipment qualification, seismic response screening, vehicle mounts, payload isolation, machine foundations and laboratory shaker testing.

It helps answer practical questions:

does a mount reduce transmitted force at operating speed;
does a floor motion amplify payload acceleration;
does a machine skid pass vibration into a building;
does a test fixture over-amplify a device at a resonance;
does a measured acceleration ratio match the assumed isolation model.

For a damped single-degree-of-freedom system with frequency ratio:

\displaystyle r=\frac{f}{f_n}

and damping ratio $\zeta$ , a common force transmissibility expression is:

\displaystyle T_R=\frac{\sqrt{1+(2\zeta r)^2}}{\sqrt{(1-r^2)^2+(2\zeta r)^2}}

For harmonic base displacement $y(t)$ and absolute mass displacement $x(t)$ , the absolute motion transmissibility has the same magnitude form:

\displaystyle \left|\frac{X}{Y}\right|=\frac{\sqrt{1+(2\zeta r)^2}}{\sqrt{(1-r^2)^2+(2\zeta r)^2}}

The relative displacement across the isolator $z=x-y$ has a different ratio:

\displaystyle \left|\frac{Z}{Y}\right|=\frac{r^2}{\sqrt{(1-r^2)^2+(2\zeta r)^2}}

That distinction matters. A mount can reduce transmitted force while still allowing large relative travel, or it can limit relative travel while transmitting more high-frequency force.

Measurement Convention

A transmissibility value is only useful when the numerator and denominator are explicit. For measured acceleration transmissibility between a payload and a base:

\displaystyle T_a(f)=\left|\frac{A_{payload}(f)}{A_{base}(f)}\right|

For force transmissibility through a mount:

\displaystyle T_F(f)=\left|\frac{F_{transmitted}(f)}{F_{input}(f)}\right|

Those ratios answer different questions. A low acceleration ratio at one sensor does not prove that transmitted force is low, and a low force ratio does not prove that relative isolator travel is acceptable. Test reports should state sensor locations, directions, units, phase convention and whether the values come from operating data, shaker input, impact test data or a model.

Parallel paths are a common reason measured transmissibility does not match the simple isolator formula. Pipes, cables, hard stops, skid contact, fixture bolts and flexible floors can bypass the intended mount. If the measured ratio is higher than predicted, the first review should check the load path and boundary condition before changing damping or stiffness values in the model.

Worked Example: Amplification and Isolation

A machine runs on isolators. The mounted natural frequency is:

f_n=8.0\ \text{Hz}

The damping ratio is:

\zeta=0.08

First check operation near a problematic startup speed:

f=8.5\ \text{Hz}

The frequency ratio is:

\displaystyle r=\frac{8.5}{8.0}=1.0625

The damping term is:

2\zeta r=2(0.08)(1.0625)=0.170

Force transmissibility is:

\displaystyle T_R=\frac{\sqrt{1+0.170^2}}{\sqrt{(1-1.0625^2)^2+0.170^2}}

\displaystyle T_R=\frac{1.014}{0.213}=4.75

In decibels:

20\log_{10}(4.75)=13.5\ \text{dB}

Engineering comment: the isolators amplify transmitted force near resonance. Calling the installation an “isolation system” is misleading at this speed. The engineer should review startup dwell time, support stiffness, damping, flexible services, frame modes and measured vibration.

Now check steady operation at:

f=30\ \text{Hz}

The frequency ratio is:

\displaystyle r=\frac{30}{8.0}=3.75

The damping term is:

2\zeta r=2(0.08)(3.75)=0.60

Transmissibility becomes:

\displaystyle T_R=\frac{\sqrt{1+0.60^2}}{\sqrt{(1-3.75^2)^2+0.60^2}}

\displaystyle T_R=\frac{1.166}{13.08}=0.089

In decibels:

20\log_{10}(0.089)=-21.0\ \text{dB}

Engineering comment: at 30 Hz the simplified model predicts attenuation. Only about $8.9\%$ of the harmonic force is transmitted through the idealized isolator path. In the real installation, parallel paths through pipes, cables, stops, baseplate contact, floor flexibility or fixture stiffness can make the measured transmissibility higher than the model.

Transmissibility is not vibration isolation. Vibration isolation is the design method or system objective. Transmissibility is a measured or calculated ratio used to judge whether the system amplifies or attenuates vibration.

Transmissibility is not a frequency response function in the most general sense. An FRF may have physical units such as acceleration per newton. Transmissibility is usually a dimensionless response ratio between comparable input and output quantities.

Transmissibility is not damping ratio. Damping ratio affects the resonance peak and high-frequency trend, but it is not itself the output/input response ratio.

Transmissibility is not natural frequency. Natural frequency sets where amplification is likely. Transmissibility states the actual ratio at a given frequency, damping level, input type and measurement path.

Transmissibility is not effective modal mass. Effective modal mass says how strongly a mode participates in a direction. Transmissibility says how much response is passed from one point, support or quantity to another.

Validation and Common Mistakes

A defensible transmissibility value states input quantity, output quantity, sensor locations, directions, frequency, amplitude convention, phase convention, boundary condition, operating state, damping assumption, frequency resolution, calibration and whether the ratio is force, absolute motion, relative motion or acceleration transmissibility.

Common mistakes include:

reporting “the transmissibility” without saying force, motion, acceleration or relative displacement;
using force transmissibility formulas for base-motion response without checking the convention;
assuming values below 1 at one frequency mean the system isolates everywhere;
ignoring resonance amplification during startup, shutdown or transient dwell;
adding damping to reduce the resonance peak while increasing high-frequency transmitted force;
measuring input and output with sensors in different directions or incompatible units;
ignoring parallel transmission paths through pipes, cables, hard stops, fixtures or floor flexibility;
comparing model and test ratios without checking whether the measured ratio is peak, RMS, narrowband, broadband or averaged.

REF

Disciplines

Transmissibility

Definition

Engineering Role

Measurement Convention

Worked Example: Amplification and Isolation

Validation and Common Mistakes

See also

Engineering Role

Measurement Convention

Worked Example: Amplification and Isolation

Distinction from Related Terms

Validation and Common Mistakes