Glossary term

Base Excitation

Imposed support or foundation motion that excites a structure through inertial loading rather than through a directly applied force at the response mass.

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

Definition

concept

Base excitation is dynamic loading caused by imposed motion of a support, base or foundation rather than by a force applied directly to the responding mass.

In a base-excited system, the input is support displacement, velocity or acceleration. The structure responds because its inertia resists that imposed motion, creating relative displacement, internal force and transmitted vibration. Base excitation is common in seismic analysis, shaker-table tests, vehicle road input, machinery floor vibration, payload isolation and equipment qualification.

Base excitation occurs when a structure is driven by motion at its support or foundation. The input is not a force applied directly to the mass. It is imposed displacement, velocity or acceleration at the base.

For a simple mass-spring-damper system with absolute mass displacement $x(t)$ and base displacement $y(t)$ , the equation of motion can be written as:

m\ddot{x}+c(\dot{x}-\dot{y})+k(x-y)=0

Using relative displacement:

z=x-y

the same model becomes:

m\ddot{z}+c\dot{z}+kz=-m\ddot{y}

This form shows the engineering meaning: base acceleration creates an equivalent inertial excitation. The support motion drives the system through inertia, relative motion, spring force and damping force.

Engineering Role

Base excitation is common when the environment moves the support rather than pushing directly on the component being assessed. Examples include earthquake ground motion, shaker-table tests, vehicle road input, ship foundation motion, building floor vibration, rotating-machinery skid motion, spacecraft launch vibration and payload isolation.

The distinction from force excitation matters because the input measurement, model equation, transmissibility definition and validation method change. A force-input modal shaker test measures applied force at a drive point. A base-excited test measures imposed support motion and response at the mounted item. Treating one as the other can give wrong load paths, wrong phase interpretation and wrong design margins.

Engineers often use base excitation to evaluate:

absolute acceleration of equipment or payloads;
relative displacement across mounts, isolators or clearances;
transmitted force into a support;
modal participation under a ground or support acceleration direction;
seismic, road, launch, floor or machinery foundation response;
whether sensors and data acquisition capture the actual input motion.

Input Convention and Response Coordinates

Base excitation can be specified as displacement, velocity or acceleration. Those inputs are related for harmonic motion, but they are not interchangeable without frequency:

A_y=\omega^2Y

and:

V_y=\omega Y

where $Y$ , $V_y$ and $A_y$ are base displacement, velocity and acceleration amplitudes. A small displacement at high frequency can imply a large acceleration, while a large low-frequency displacement can imply a modest acceleration. The test report should state which quantity is controlled and which quantity is measured.

Response coordinates must also be explicit. Absolute response $x(t)$ describes motion in an inertial frame. Relative response $z(t)=x(t)-y(t)$ describes motion across mounts, isolators or clearances. Equipment qualification often cares about absolute acceleration, while isolator stroke and mechanical interference depend on relative displacement.

Worked Example: Convert Base Acceleration to Relative Motion

A small instrument is mounted on isolators. During a shaker-table screening test, the base acceleration amplitude is:

A_y=0.30g=0.30(9.81)=2.943\ \text{m}/\text{s}^2

The excitation frequency is:

f=12\ \text{Hz}

The mounted natural frequency and damping ratio are:

f_n=8.0\ \text{Hz},\quad \zeta=0.05

The circular frequency is:

\omega=2\pi f=2\pi(12)=75.40\ \text{rad}/\text{s}

For harmonic motion, acceleration amplitude and displacement amplitude are related by:

A_y=\omega^2Y

so the base displacement amplitude is:

\displaystyle Y=\frac{A_y}{\omega^2}=\frac{2.943}{75.40^2}=5.18\times10^{-4}\ \text{m}=0.518\ \text{mm}

The frequency ratio is:

\displaystyle r=\frac{f}{f_n}=\frac{12}{8.0}=1.50

The denominator that appears in the single-degree-of-freedom base-response ratios is:

D=\sqrt{(1-r^2)^2+(2\zeta r)^2}

Substitute the values:

D=\sqrt{(1-1.50^2)^2+(2(0.05)(1.50))^2}=1.259

The relative displacement ratio is:

\displaystyle \left|\frac{Z}{Y}\right|=\frac{r^2}{D}=\frac{1.50^2}{1.259}=1.787\approx1.79

Therefore:

Z=1.787(0.5177)=0.925\ \text{mm}

The absolute displacement ratio is:

\displaystyle \left|\frac{X}{Y}\right|=\frac{\sqrt{1+(2\zeta r)^2}}{D}=\frac{\sqrt{1+0.150^2}}{1.259}=0.803

so:

X=0.803(0.5177)=0.416\ \text{mm}

If the mounted instrument mass is $20\ \text{kg}$ , the base acceleration corresponds to an equivalent inertial-force amplitude:

F_{eq}=mA_y=20(2.943)=58.9\ \text{N}

Engineering comment: the base displacement is only $0.518\ \text{mm}$ , but the relative motion across the isolator is about $0.925\ \text{mm}$ because the excitation is above the mounted natural frequency but still close enough for dynamic amplification. The equivalent inertial force is useful for intuition, but the real load path is support motion, not a direct external force applied at the instrument.

Base excitation is not transmissibility. Base excitation is the input condition. Transmissibility is the output/input ratio used to interpret the response.

Base excitation is not a force-input modal shaker test. A force-input test measures applied force at a drive point. A base-excited test imposes support motion and measures response relative to that motion.

Base excitation is not effective modal mass. Effective modal mass tells how strongly a mode participates in a specified input direction. Base excitation is one kind of input that can make that participation important.

Base excitation is not a boundary condition by itself. The support motion must be paired with a model boundary, coordinate convention, input direction and measured or specified time history.

Base excitation is not just seismic loading. Earthquake ground motion is an important example, but base excitation also appears in vehicles, machines, aircraft equipment, ships, test fixtures and precision instruments.

Validation and Common Mistakes

A defensible base-excitation model or test states the input quantity, support location, direction, coordinate frame, acceleration/displacement convention, fixture stiffness, mass properties, damping, boundary condition, frequency band, sensor calibration, sampling rate, anti-alias filtering and whether response is absolute or relative.

Common mistakes include:

applying a force-input formula to a support-motion problem;
using base acceleration without converting units or checking the implied displacement;
confusing absolute response $x$ with relative response $z=x-y$ ;
ignoring fixture flexibility, table control error, floor modes or parallel load paths;
treating a single-axis base input as representative of all translational and rotational directions;
using effective modal mass without documenting the influence vector;
comparing model and test without matching support motion, damping, boundary conditions and response coordinates;
assuming linear scaling when isolators, stops, friction, cable restraint or clearances make the response nonlinear.

REF

Disciplines

Base Excitation

Definition

Engineering Role

Input Convention and Response Coordinates

Worked Example: Convert Base Acceleration to Relative Motion

Validation and Common Mistakes

See also

Engineering Role

Input Convention and Response Coordinates

Worked Example: Convert Base Acceleration to Relative Motion

Distinction from Related Terms

Validation and Common Mistakes