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Appendix 3. Engine Vibration Resonance Effects

Version 1.5 of the Shaker software adds engine vibration resonance effects.

In some aircraft powering-up the engines may cause higher vibration magnitudes at lower than maximum speeds as a result of the engine running frequency passing through resonant frequencies of the supporting airframe.

This effect is modelled in V1.5 by adding a simple forced damped vibration model to the engine vibration output.

When enabled the engine vibration strength is magnified as the engine frequency increases with engine speed and approaches and passes through the damped natural frequency of the structure. The response is as shown in the graph below - it shows magnification factor v frequency ratio.

Frequency Ratio is the ratio of current engine vibration frequency to the specified resonant frequency.

There are two user settings:

1. Damping Ratio: this sets how much damping is in the system and is typically in the range 0.1 to 1.0. It controls the size of the magnification factor Q.

Smaller values indicate weaker damping and therefore higher peak vibration amplitudes (see the effect of different R values in the graph).

When this setting is changed the Maximum Magnification Factor is recalculated and displayed (Max Mag Fac). This can be used as a guide to help choose your damping ratio.

2. Resonant Frequency (Hz): Set this to define the approximate frequency at which the magnification will be strongest.

(Tip: observe the frequency (CPS) of the engine vibrations whilst running up the engines to see the possible range for this setting.)

At lower values of Damping Ratio (smaller R) the point of maximum magnification will be close to the specified resonant frequency (see the dotted line in the graph), however as damping ratio approaches 1.0 the point of maximum magnification drops below the resonant frequency.

For the purposes of this application the magnification factor is capped at 5.0. This puts a limit on very high peaks that are simply clipped by the driver card.

NOTE: the base vibration amplitude remains as normally calculated - ie amplitude is proportional to engine fuel flow (this is a proxy for engine power). Vibration frequency is proportional to engine speed.  When resonance is enabled the final output vibration amplitude is then the base amplitude x the magnification factor.

The live magnification factor is displayed in the blue progress bar.

The overall effect of the feature can be to produce an engine vibration feel which is stronger at lower engine speed and then reduces when the engine reaches normal operating speeds. This is most noticeable when powering-up the engines for take-off.

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