Understand Impulse response help

Hola file exchange team!

I am having trouble understanding the impulse response function.

I have a beam of 10 m long. I place 2 sensors, one at point A and one at point B. I then excite the beam at point E (shown in picture) by tapping it with a hammer. I then repeat this on several different beams of different lengths, dimensions, materials and more. I want to tap the beam to see how the beam responds, using accelerometers at locations a and b, and see if I can estimate things about the beam (example material).

In the case of calculating impulse response, what exactly is my input? I assume it is the excitation signal, however I do not measure the excitation signal until it gets to point A (there is no sensor at point E). I therefore do not know the excitation at the source, it just be with a hammer hitting the beam. The matlab documentation uses inputs as an example, but this does not mean anything to me as I do not know my input.

Also, what does the impulse response actually tell me? How is this useful?

Gracias todos,

Ben

[Star Strider]

It appears that you are doing system identification of a linear model. See the Linear Model Identification documentation for details.

[Optics Wizard]

Quick concept tutorial on impulse functions:

Let's say the sensors A and B are measuring the vertical displacement of your horizontal beam. Let's assume the hammer is hitting at point E upward. When the hammer hits, the beam is nearly-instantaneously moved up at point E. Assuming something is keeping the beam generally in place, the beam is nearly-instantaneously bent. The beam will have tension on the bottom of it and compression at the top, so the beam will spring back. The springing function will form resonant modes in the beam, wobbling A and B up and down until friction gradually causes the beam to settle again.

The impulse function is the hammer, possibly defined by how much vertical displacement occurs at point E at time t=0. The beam is bent along the entire length assuming it is kept in place somewhere. For instance, the far side from E might be fixed. When the impulse function happens, there will also be displacement at A and B.

The impulse response shows what modes are in the beam. For instance, if you don't know where the beam is fixed, you might learn which parts of the beam are fixed or whether the beam is uniform. Once the impulse response is known, you can model the entire beam for different amplitudes of impulse functions at different times. For instancem, if you know the impulse response function perfectly, you can hit the hammer multiple times and know exactly what shape the beam will be at some later time.

[Ben]

Hola Optics Wizard, thank you for your explanation. I have some questions, in response to this, I hope you can answer.

1. If the hammer at point E is the impulse, how do I define this input in matlab, when I consider that I am not measuring anything at point E? Is it possible to include a model signal which defines the impulse at E? I believe the code would be something like IRF=impulse(modelledSignal,output).
2. However, I have many different outputs depending on the conditions - there are many samples taken at point A and B along the beam and samples A and B change depending on the material of the beam, length etc. How do I define the impulse response for all of these? Are they to be done serpately and then averaged?

Muchas gracias, I appreciate the help. Ben