Library / Structural dynamics and vibration testing / SDY-35
Structural dynamics and vibration testing
Accelerance from a measured receptance
Acceleration per unit force obtained from a displacement-per-force frequency response by multiplying by −ω².
- Ref
- SDY-35
- Rev
- v1
- Field
- Structural dynamics and vibration testing
- Result
- |A| [(m/s²)/N]
Accelerance (inertance) is acceleration per unit force. Two time derivatives of displacement give A = −ω²H: the magnitude is ω²|H| and the phase shifts by 180°. Here H is in mm/N and the accelerance is returned in (m/s²)/N. It is the quantity measured by an accelerometer and a force hammer.
Acceleration per unit force obtained from a displacement-per-force frequency response by multiplying by −ω². This entry returns the magnitude; the phase shifts by 180°.
Calculator
- Real part of A−0.8 (m/s²)/N
- Imaginary part of A0.4 (m/s²)/N
- Mobility magnitude, |A|/ω0.04472 (m/s)/N
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 20 rad/s the accelerance is 0.8944 (m/s²)/N.
- Accelerance grows with the square of frequency for a given receptance, which is why accelerometer data emphasise the high-frequency modes.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing ((m/s²)/N) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ω Angular frequency | 1 to 200 rad/s | 0.002236 | 89.44 | 89.44 | +10% | +21 % |
| Re H Real part of the receptance | −5 to 5 mm/N | 0.4 | 2.04 | 1.64 | +0.2 mm/N | +8.07 % |
| Im H Imaginary part of the receptance | −5 to 5 mm/N | 0.8 | 2.154 | 1.354 | +0.2 mm/N | −3.67 % |
Sweep of Angular frequency
| Angular frequency (rad/s) | Accelerance magnitude ((m/s²)/N) |
|---|---|
| 1 | 0.002236 |
| 25.88 | 1.497 |
| 50.75 | 5.759 |
| 75.63 | 12.79 |
| 100.5 | 22.58 |
| 125.4 | 35.15 |
| 150.3 | 50.48 |
| 175.1 | 68.58 |
| 200 | 89.44 |
Sweep one variable
Variables and how each one contributes
Accelerance magnitude
What the equation gives you. Everything else feeds it.
Angular frequency
The angular frequency, in rad/s (2π times the frequency in Hz). Scales the converted magnitude in proportion (mobility) or with its square (accelerance). Raising it by 10 % (to 22) moves the result by +21 %, from 0.8944 to 1.082 (m/s²)/N.
Real part of the receptance
The real part of the receptance, in mm/N: displacement per unit force. Raises the magnitude of the converted response. Raising it by 0.5 (to 2.5) moves the result by +20.4 %, from 0.8944 to 1.077 (m/s²)/N.
Imaginary part of the receptance
The imaginary part of the receptance, in mm/N. Raises the magnitude of the converted response. Raising it by 0.5 (to −0.5) moves the result by −7.8 %, from 0.8944 to 0.8246 (m/s²)/N.
Worked example with the values above
- Receptance magnitude: |H| = 2.2361 mm/N = 0.0022361 m/N.
- Multiply by ω² = 400 (rad/s)².
- |A| = 0.89443 (m/s²)/N.
Assumptions and limits
- Averaged spectra from the same records, windows and frequency bin, with a stationary, linear system.
- At least several averages are used, because a single unaveraged record gives a coherence of one at every frequency.
Common mistakes
- Using H1 where the force channel is noisy, which biases the peak low, or H2 where the output is noisy.
- Reading frequency response values where the coherence is low.
- Forgetting the 90° and 180° phase changes when converting between receptance, mobility and accelerance.
Statistics and uncertainty
Spectral estimates carry random error that falls as the square root of the number of averages and bias that depends on leakage and noise. Quote the number of averages, and read the coherence before relying on any frequency response value.
Where it is used
- Estimating frequency response functions from impact hammer and shaker tests.
- Converting between displacement, velocity and acceleration responses for modal fitting and coupling.
Maths you need
- Cross-spectrum: the averaged product of one signal and the conjugate of another
- Complex numbers: real and imaginary parts, magnitude and phase
- Frequency response function: output per unit input at each frequency