Status: educational explainer. This page reports no experiment results. Project S.P.H.E.R.E. is at the proposal stage, hypotheses are not findings, and nothing here amends the draft LOC-1 protocol.

Terms

Natural frequency (eigenfrequency)

A frequency at which a structure vibrates freely, set by its mass, stiffness, geometry and constraints. Each mode has its own.

Resonance

The large response that appears when a structure is driven at or near a natural frequency.

Mode and mode shape

A mode is a pattern of motion that repeats at one frequency. Its mode shape is the spatial pattern, such as which parts of a sphere move in and out and which stay still.

Breathing mode

The radial mode of a sphere in which the whole surface moves in and out together.

Degenerate modes and mode splitting

In a perfect sphere, groups of modes with different orientations share one frequency. Imperfections in shape, thickness or material split them into nearby peaks.

Node and antinode

A node is a point a mode does not move; an antinode is where it moves most. Where a mass or support is placed relative to these decides how much it matters.

Damping ratio (ζ)

A measure of how quickly vibration dies away. For light damping ζ ≈ 1/(2Q).

Quality factor (Q)

Q ≈ f0/Δf, where Δf is the half-power bandwidth of a resonance peak. Higher Q means a narrower peak and a longer ring-down.

Half-power bandwidth and linewidth

The width of a resonance peak between the points where power falls to half of the peak, or amplitude to 1/√2. It sets how precisely a frequency can be located.

Frequency response function (FRF)

The complex ratio of response to input force as a function of frequency. It carries both magnitude and phase.

H1 estimator

An FRF estimate formed as the input–output cross-spectrum divided by the input auto-spectrum, which suppresses uncorrelated noise on the output.

Coherence

A value between 0 and 1 at each frequency showing how much of the output is linearly related to the measured input. Low values flag noise, nonlinearity or unmeasured inputs.

A number between 0 and 1 comparing two mode shapes, MAC = |φaTφb|2 / ((φaTφa)(φbTφb)). Near 1 means the same shape.

Operating deflection shape

The motion pattern of a structure at a given frequency under a particular drive. It is not necessarily a pure mode.

Linear time-invariant (LTI) system

A system whose response is proportional to its input and does not change over time. Impulse responses and FRFs fully describe it.

Nonlinearity

Behaviour in which frequency, damping or shape depends on vibration amplitude, producing harmonics and level-dependent peaks.

Mass loading

Shift and damping added to a structure by sensors, adhesive and mounts, large for light structures.

Aliasing and the Nyquist limit

Energy above half the sampling rate folds back into the measured band. The sampling rate must exceed twice the highest frequency present, and an analog anti-aliasing filter should remove energy beyond that.

Impulse response

The output of a system after an ideal instantaneous input. Its Fourier transform is the transfer function.

Deconvolution

Dividing out a known input from a recorded output to recover the system response, for example with an inverse filter after a sine sweep.

Time reversal

Recording a response, reversing it in time and re-emitting it so that waves refocus at the original point. It focuses energy; it does not change natural frequencies.

Spillover

In active control, the unwanted excitation of modes that the controller did not model when it acts on the modes it did.

Thin-shell (ring) frequency

The frequency near which a thin shell's membrane (breathing) behaviour gives way to bending-dominated behaviour; for a thin spherical shell the breathing mode is about (1/2πR)√(2E/ρ(1−ν)).

Sources

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