Measurement methods · What is vibrating?

Modes, nodes and peak identification

How do we know which vibration a frequency belongs to?

A mode includes a spatial shape as well as a natural frequency and damping. The identification matters because inversion formulas assume a particular family and order of vibration.

Try the interactive demo

Start with something familiar

A skipping rope can form one large loop or several smaller loops. These patterns help visualize modes. A vibrating wood strip also has different patterns, although bending beams do not follow the same frequency ratios as a stretched rope.

Colored salt forms branching nodal patterns on a vibrating metal Chladni plate — Connect the diagram to a real object
In this real Chladni experiment, colored salt gathers along nodal lines of a vibrating metal plate. The pattern helps make a mode visible; a wooden specimen needs its own mode identification and boundary conditions.
Carlos Andrés Reyes · Wikimedia Commons · CC BY 2.0
Article photographs retain their full proportions; covers show a cropped view.

Bending mode 1

Red dots: displacement nodes

Bending mode 2

Red dots: displacement nodes

Diagram · Displacement nodes divide a bending pattern into regions moving in opposite directions. The illustrated displacement is exaggerated.

Notice what changes
A mode is a spatial pattern, not just a pitch. Some locations move strongly while the displacement nodes scarcely move for that mode.
Understand why
Where you tap matters. A tap at a node gives weak participation of that mode; tapping an antinode can make it easier to excite. This does not remove other modes from the object.
Connect it to wood and making
A modulus formula expects a named mode. Identifying the wrong family or order changes the inference even if the peak frequency itself is read accurately.

Put names to the ideas

Shape, frequency and loss

In a linear modal description, each mode has a characteristic displacement pattern. Two peaks near each other may correspond to different bending directions, torsion or structural coupling.

Nodes are quiet locations

Tapping at a displacement node weakly excites that mode; observing there can also suppress it. Moving the tap or microphone tests whether a peak responds as the assumed shape predicts.

Order is model-specific

A free beam’s rigid translation and rotation are zero-frequency motions, not its first bending resonance. Do not substitute a plate Mode 5 frequency into a first-bending-beam formula.

u(x,t)\approx\sum_n\phi_n(x)q_n(t)

φn describes the shape of mode n; qn describes how strongly that shape moves over time. The sum means several patterns can be present in one recording.

A worked example

For the same ideal uniform beam, rotating the bending direction exchanges the relevant width and thickness. A second strong peak can therefore be another bending family rather than a harmonic.

Explore it yourself

Repeat the test at several tap and support positions. Compare the observed response with the boundary-condition explorer before selecting a frequency.

Bending mode

Tap position % L

Relative point-force coupling: 0.608
Selected position: 50.00 % L

The value is |φ(x)| for a point force, not the actual amplitude of a recording. Mass, damping, force spectrum and the observing position also affect measured peaks.

Check your understanding

A peak gets weak after moving the tap. Does the mode necessarily disappear?No: its excitation may have become weakerYes: tap position removes a natural mode

Start with something familiar

Connect the diagram to a real object

Bending mode 1

Bending mode 2

Notice what changes

Understand why

Connect it to wood and making