Modal Test Fundamentals

What Is It?

A modal test is an experimental procedure that identifies the dynamic characteristics of a structure — its natural frequencies, damping ratios and mode shapes — by exciting the structure with a known input and measuring the response at multiple locations. The fundamental output of a modal test is the frequency response function (FRF): the ratio of response to input as a function of frequency. The peaks in the FRF reveal the natural frequencies; the sharpness of the peaks reveals the damping; the relative amplitudes and phases across measurement locations reveal the mode shapes. Together, these three quantities — frequency, damping and mode shape — completely characterise the linear dynamic behaviour of the structure and provide the data for correlation with the finite element model's modal analysis results.

Why It Matters

Modal testing is the primary experimental method for validating the dynamic properties of a structural model. A finite element modal analysis predicts natural frequencies and mode shapes; the modal test measures them. If they agree, the model's mass and stiffness distribution are correct, and the model can be used for dynamic response prediction — harmonic, random, transient and shock. If they disagree, the mass or stiffness representation is wrong, and the model cannot be trusted for any dynamic analysis. Modal testing is particularly powerful because the dynamic properties are global — they are sensitive to the overall mass and stiffness distribution, not to local detail. A single modal test can validate the global dynamic model in a way that no static test can.

Modal testing validates the global mass and stiffness distribution of the model. A model that predicts the right frequencies and mode shapes has the right global dynamic behaviour — and can be used for dynamic response prediction with confidence.

Excitation Methods

The structure must be excited to reveal its dynamic properties. Two excitation methods dominate engineering practice: the impact hammer and the electrodynamic shaker. Each has advantages and limitations, and the choice depends on the structure, the frequency range of interest and the desired signal quality.

The Impact Hammer

The impact hammer is the simplest excitation device. It consists of a hammer head with a force transducer at the tip and a selection of tip materials of varying hardness. When the hammer strikes the structure, the force transducer measures the impulse, and the hardness of the tip determines the frequency content of the impulse — a hard tip produces a short, broadband impulse that excites high frequencies; a soft tip produces a longer, narrower impulse that concentrates energy at low frequencies. The hammer is portable, requires no fixture and can excite the structure at any accessible point. Its limitation is energy: a hammer blow delivers limited total energy, so the response at low frequencies or on large, heavily damped structures may be too weak to measure. The hammer is ideal for small to medium structures, for preliminary surveys and for excitation at multiple locations without reconfiguration.

Impact hammer test set-up:

  Structure with accelerometers
  ┌──────────────────────┐
  │   [acc]      [acc]   │
  │     \         /      │
  │      \        /      │
  │  ────┴───────┴────   │  ← measurement locations
  │                      │
  └──────┬───────────────┘
         │
    ↓ ↓ ↓  ← hammer strike (roving input)
    │
  [Force transducer]
     ↓
  Impact hammer
     ↓
  Signal → FFT analyser

  Input:  force (measured at hammer tip)
  Output: acceleration (measured at each accelerometer)
  FRF = Output / Input  vs  frequency

The Electrodynamic Shaker

The electrodynamic shaker applies a controlled force to the structure through a stinger rod — a thin, flexible rod that transmits axial force but minimises lateral stiffness. The shaker is driven by a power amplifier fed with a signal generator, and the force is measured by a load cell between the stinger and the structure. The shaker can apply any waveform — sinusoidal, random, burst random, chirp — and can deliver significantly more energy than a hammer. The shaker is fixed at one location (or a few locations for multi-shaker testing) and the response is measured at many locations. The shaker's limitation is the stinger: it adds mass and stiffness to the structure, potentially altering the dynamics, and it requires a fixture to mount the shaker. The shaker is ideal for medium to large structures, for low-frequency testing where hammer energy is insufficient and for tests requiring high-quality FRFs.

The shaker stinger is an appended mass and stiffness on the test structure. For lightweight structures or higher modes, the stinger can shift frequencies and distort mode shapes. Use a light, stiff stinger, or include the stinger in the analytical model used for correlation.

The Frequency Response Function

The frequency response function (FRF) is the fundamental measured quantity in a modal test. It is the ratio of the structural response (acceleration, velocity or displacement) to the applied force, expressed as a function of frequency. The FRF is computed from the measured input force and output response using the fast Fourier transform (FFT). At each frequency, the FRF gives the complex ratio of response amplitude to force amplitude, including both magnitude and phase. The FRF is the transfer function of the structure — it completely characterises the linear dynamic behaviour from the input point to the output point.

Frequency response function (H1 estimator):

H(ω)  =  G_xy(ω)  /  G_xx(ω)

where:
H(ω)     =  frequency response function (complex)
G_xy(ω)  =  cross-spectral density of input x and output y
G_xx(ω)  =  auto-spectral density of input x
ω        =  angular frequency (rad/s)

At a natural frequency, |H(ω)| peaks — the structure resonates.
The width of the peak determines the damping.
The phase shifts by approximately 90° through resonance.

Extracting Modal Parameters

From the measured FRFs, the modal parameters — natural frequencies, damping ratios and mode shapes — are extracted by a process called modal parameter estimation. Several methods are available, ranging from simple peak picking to sophisticated multi-degree-of-freedom curve fitting. The principle is the same: the measured FRF is modelled as the sum of individual modal contributions, each characterised by a frequency, damping and residue (related to the mode shape amplitude). The curve-fitting algorithm adjusts the modal parameters to minimise the difference between the measured FRF and the modal model. The result is a set of modes, each with a natural frequency, a damping ratio and a mode shape vector defined at the measurement locations.

• Peak picking — simplest method; identifies frequencies at FRF peaks, estimates damping from peak width; suitable for well-separated modes
• Circle fit — fits a circle to the Nyquist plot of the FRF near each resonance; gives frequency, damping and residue
• Poly-reference — fits multiple FRFs simultaneously; separates closely spaced modes; uses all references and responses
• Complex mode indicator function (CMIF) — uses singular value decomposition of the FRF matrix to identify modes and their multiplicity
• Stabilisation diagram — plots identified poles as the model order increases; stable poles indicate physical modes, unstable ones indicate noise

Mode Shape Measurement

The mode shape is the deformation pattern of the structure at a natural frequency. It is measured by recording the FRF at multiple response locations for a fixed input (or vice versa) and extracting the relative amplitude and phase at each location for each mode. The number and placement of measurement locations determine the spatial resolution of the mode shape. Too few locations, and the mode shape is aliased — a higher mode may appear as a lower mode because the measurement grid cannot resolve its wavelength. The rule of thumb is that a mode shape requires at least five measurement points per half-wavelength to be adequately resolved. For complex structures, this can mean hundreds of measurement locations, typically instrumented with roving accelerometers or with a scanning laser Doppler vibrometer.

MISTAKE: Using too few measurement locations to resolve higher modes. A measurement grid that cannot resolve the wavelength of a mode will alias it — the mode appears as a different, lower mode shape. Use at least five points per half-wavelength for each mode of interest.

Support Conditions for Modal Testing

The support condition in a modal test profoundly affects the measured modes. If the structure is tested on its operational supports — bolted to its mounting structure, for example — the measured modes include the dynamics of the mounting structure and the interface stiffness. This may be desired if the in-service dynamics are the target, but it complicates correlation because the mounting structure must also be modelled. The alternative is free-free support — suspending the structure on soft springs or bungees so that the structure is effectively unconstrained. In a free-free condition, the first six modes are rigid-body modes at near-zero frequency, and the first flexible mode is purely a property of the structure. Free-free testing eliminates the boundary condition from the correlation problem and is the preferred approach for modal validation of the structure itself.

Practical Considerations

A successful modal test requires attention to several practical details that determine the quality of the measured data and the reliability of the extracted modal parameters.

• Choose excitation method based on structure size, frequency range and energy requirements — hammer for small structures, shaker for large
• Place the excitation point away from mode shape nodes — if the input is at a node of a particular mode, that mode will not be excited
• Use enough response locations to resolve all modes of interest — at least five points per half-wavelength
• Average multiple measurements to improve signal-to-noise — typically 8–32 averages for hammer, more for low-energy random excitation
• Use windows to reduce leakage — force/exponential windows for hammer, Hanning window for random excitation
• Check reciprocity — the FRF from point A to point B should equal the FRF from point B to point A; non-reciprocity flags a problem
• Check the coherence function — coherence below 0.9 at a frequency indicates poor signal-to-noise or non-linearity at that frequency
• Use a stabilisation diagram to distinguish physical modes from noise — include only stable, consistently identified modes in the correlation

Key Takeaways

• A modal test identifies natural frequencies, damping ratios and mode shapes from measured FRFs
• Modal testing validates the global mass and stiffness distribution of the structural model
• The impact hammer is simple and portable but limited in energy — suited to small and medium structures
• The electrodynamic shaker delivers controllable energy but introduces a stinger mass and requires a fixture
• The FRF is the fundamental measured quantity — the complex ratio of response to input versus frequency
• Modal parameters are extracted by curve-fitting the measured FRFs with a modal model
• Mode shape measurement requires enough locations to resolve the wavelength — at least five per half-wavelength
• Free-free support eliminates boundary effects and provides the cleanest correlation for structure-only validation
• Check coherence and reciprocity as quality indicators throughout the test