With an appropriately collocated accelerometer is it possible to retrieve lateral deflection of a beam under static loading.

The beam will be loaded and then deflect until it reaches equilibrium with external load. Could one integrate accelerometer signal twice to obtain how much has a point been deflected?

This theoretically in the framework of an Euler-Bernoulli beam under pure bending.


2 Answers 2


The short answer would be no, or at least not reliably. In case of an actual static load there is no time dependency, hence no acceleration and thus no signal to integrate.

You could try to use the transient response of the beam being loaded and try to integrate that twice in order to determine the deflection. Typically, it is difficult to accurately determine absolute displacement in this way. Most accelerometers cannot (accurately) measure DC signals and the inherent noise level of the sensor might cause problems if the signal amplitude is too low. Depending on your accuracy requirements the resulting answer might or might not be acceptable.

If your goal is to determine deflection you are probably better of with an appropriate position sensor.

  • $\begingroup$ how would you use a position sensor to measure lateral deflection? $\endgroup$
    – benr
    Oct 20, 2020 at 19:21
  • $\begingroup$ @BenRomarowski Maybe a strain gauge. $\endgroup$
    – Eric S
    Oct 21, 2020 at 2:25
  • $\begingroup$ A strain gauge or maybe a capacitive displacement sensor should work. $\endgroup$
    – user883521
    Oct 21, 2020 at 10:44

Double integration of acceleration over time

Double integration with an accelerometer would not yield any useful results under static loading.

Alternative approach

What you could do instead is the following (the longer the beam the better - a bridge would be ideal for this):

  • place a few accelerometers along one side of the beam (if you can place on top and bottom even better). You'd also need to know the exact position along the beam for each accelerometer.

  • from each accelerometer, you estimate the change in angle. you need to take two measurements :

    • no load
    • static load (apply the load, wait to stabilise and then start to measure).

Since load is static you can measure over a long time and get a quite accurate measurement. Essentially what you are measuring is the rotation of the gravity vector.

Provided the load is uniform, or concentrated, it is now possible to perform a high order least squares fit on the angle w.r.t. to position along the beam $w'(x)$. ($w(x)$: the lateral displacement).

Then it would be possible to interpolate over the position with - I expect - meaningful results.

  • $\begingroup$ I like this idea! As long as you use an accelerometer than can measure DC signals (and hence is able to detect rotation with respect to the gravity vector) this should indeed work. The effect of random noise can be mitigated by measuring a sufficient amount of time. Not sure if this also allows you to deal with bias errors, but depending on the required accuracy that might not be relevant. $\endgroup$
    – user883521
    Oct 21, 2020 at 10:47

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