What Information Can Be Extracted from the FRF (Frequency Response Function)?
The Frequency Response Function (FRF) provides a complete description of how a system behaves across frequency. By analyzing its magnitude and phase, a wide range of physical and dynamic properties can be extracted.
1. Resonance Frequencies
Peaks in the FRF magnitude indicate resonances
- Locations of natural frequencies
- Frequencies where the system responds most strongly
Resonance frequency fr = 100Hz in this case
2. Damping Characteristics
The shape and width of resonance peaks reveal damping
- Narrow peak → low damping
- Broad peak → high damping
Quality factor Q = 100 / 15.4 ≒ 6.49351, Damping ratio ζ = 1 / (2*6.49351) ≒ 0.077
Typical calculation methods
- Half-power (-3dB) bandwidth → Half-power points occur at 1/sqrt(2) of the peak magnitude
- Curve fitting estimates damping by fitting a theoretical dynamic model to the measured FRF data
3. System Gain (Amplitude Response)
| H (f) |
Shows how much the system
input signals at each frequency → Frequency-dependent sensitivity
4. Phase Response
∠H (f)
Indicates
- phase lag between input and output
- dynamic delay
Key feature
- Rapid phase change near resonance
- Timing behavior of the system
5. Modal Properties
From FRF, we can extract intrinsic dynamic characteristics of the structure
- Natural frequencies
- Mode shapes (with multiple measurements)
- Modal damping ratios
6. System Type and Dynamics
FRF reveals whether the system behaves like physical nature of the system
- Mass dominated (high frequency)
- Stiffness dominated (low frequency)
- Damping dominated (near resonance)
| Domain | Standard FRF | Name | Inverse FRF | Name |
|---|
| Displacements | X / F | Receptance
Admittance
Dynamic Compliance
Dynamic Flexibility | F / X | Dynamic Stiffness |
| Velocity | V / F | Mobility | F / V | Mechanical Impedance |
| Acceleration | A / F | Accelerance
Inertance | F / A | Apparent Mass
Dynamic Mass |
7. Transfer Characteristics
FRF identifies
- Filters (low-pass, high-pass, band-pass, band-stop)
- Structural transmission paths → TPA (Transfer Path Analysis)
- Isolation effectiveness
Impulse response of IIR low-pass filter
FRF of IIR low-pass filter
8. Nonlinear or Measurement Issues
Although not part of FRF itself
- Low coherence value → unreliable FRF
- Indicates noise, nonlinearity, or poor excitation
Relationship between magnitude-squared coherence and FRF
Key Insight
- FRF is not just a curve—it is a complete fingerprint of the system’s dynamics
- The FRF allows extraction of resonance, damping, gain, phase, and modal properties, providing a comprehensive understanding of a system’s dynamic behavior
Conclusion
The FRF is one of the most powerful tools for understanding and quantifying system behavior in the frequency domain.
By analyzing the FRF, engineers can
- identify system characteristics
- diagnose problems
- design and validate dynamic systems
Suggested Further Reading
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What Information Can Be Extracted from the FRF (Frequency Response Function)?
The Frequency Response Function (FRF) provides a complete description of how a system behaves across frequency. By analyzing its magnitude and phase, a wide range of physical and dynamic properties can be extracted.
1. Resonance Frequencies
Peaks in the FRF magnitude indicate resonances
Resonance frequency fr = 100Hz in this case
2. Damping Characteristics
The shape and width of resonance peaks reveal damping
Quality factor Q = 100 / 15.4 ≒ 6.49351, Damping ratio ζ = 1 / (2*6.49351) ≒ 0.077
Typical calculation methods
3. System Gain (Amplitude Response)
| H (f) |
Shows how much the system
input signals at each frequency → Frequency-dependent sensitivity
4. Phase Response
∠H (f)
Indicates
Key feature
5. Modal Properties
From FRF, we can extract intrinsic dynamic characteristics of the structure
6. System Type and Dynamics
FRF reveals whether the system behaves like physical nature of the system
Admittance
Dynamic Compliance
Dynamic Flexibility
Inertance
Dynamic Mass
7. Transfer Characteristics
FRF identifies
8. Nonlinear or Measurement Issues
via Magnitude-squared Coherence
Although not part of FRF itself
Key Insight
Conclusion
The FRF is one of the most powerful tools for understanding and quantifying system behavior in the frequency domain.
By analyzing the FRF, engineers can
Suggested Further Reading
You may also find these topics helpful: