How to calculate the first mode of vibration for a glass window?

I have a window of the size 57 cm by 106 cm and 4 mm of width. I hear the loud noise from it on about 166 Hz and want to realize if it is window's self first mode of vibration that intensify this frequency (maybe even with resonance, etc.) or not.

I understand that this could depend on exact glass, fixing, etc., but is there a common idea to calculate it and have at least rough approximation?

If there is some software to calculate it (like shown in the Understanding the Finite Element Method), please advise.

  • 1
    $\begingroup$ The website at the following link claims to be able to calculate this natural frequency for you. They also show the pertinent equation. I'm not associated with this site. The various icons on the page represent different calculators (for example: fixed edges, free edges, circular plates, etc.) Scroll down on that page to see typical properties to enter for glass. calcdevice.com/rectangular-plate-vibration-frequency-id226.html $\endgroup$
    – James
    Feb 20, 2023 at 20:33
  • $\begingroup$ @James, thank you so much. This is exactly I was looking for. It gave 33 Hz which is far from 166 Hz which I experience, so I have to look at some other sources of effects. The best thing is that it shows the formula so I can see the effect's logic. If you post this comment as an answer, I'd like to mark it as "accepted correct answer". One extra thing, if you know the source of this formula (how to derive it), please give a hint, I am very interested in the problem. $\endgroup$ Feb 20, 2023 at 21:49

1 Answer 1


I am a mechanical engineer who does full time work with finite element analysis including modal analysis which involves finding the natural frequencies of structures.

Knowing the exact window dimensions is a good first step, but to calculate the exact first mode with FEM will require the two additional items listed...

  1. You need to know the density and stiffness of the glass. I don't work with glass and I'm not sure if all forms of glass have the same stiffness or not.

  2. You need to know the boundary conditions of the edges of the window. This is very important! If the window edges are held loosely, then the first mode frequency will be much lower than if the edges are held tightly.

You can likely conduct a test to find the first mode if you have a speaker and computer available. Place the speaker near the window and play a sine sweep (search for this on Youtube). Lightly place your finger on the window and you will feel vibrations when the sweep hits your first mode.

Good luck!

  • $\begingroup$ Thank you for the prompt response. As I mentioned in my question, I understand that the result will depend on stiffness ("exact glass") and boundary conditions ("fixing") and other things (temperature, etc.), but is there some solution for "average" stiffness or stiffness as a parameter and typical boundary conditions like "loose", "rubber", "steel"? I need something to start with, even rough. Again, I don't insist on FEM, I used the reference to video to show how it might look in CAD/CAM system. This could be a simple physical model of glass "box" and its vibration. $\endgroup$ Feb 20, 2023 at 18:16
  • $\begingroup$ +1, especially for the experimental approach. If you're only interested in frequency of the resonant mode, I'd follow the suggestion of using the experimental method. This way, you don't need the accurate modelling of the glass physical characteristics and, maybe more important, the boundary conditions that can affect the results. Numerical models of mechanical systems are usually "tuned"/fitted (usually on low-freq modal frequencies and shapes) with the results of experimental measurements, to get representative results $\endgroup$
    – basics
    Feb 20, 2023 at 18:21
  • $\begingroup$ @basics, I see where you coming from and, of course would try and report the results. The problem is that the original noise/vibration from the glass is so strong that I don't have a chance to overpower it with my sound sources. So, I wouldn't be able to separate the resonant caused by noise from outside from noise from my device. Neither have I a chance to move the window in silent location or find the window with the similar size in a silent location. $\endgroup$ Feb 20, 2023 at 21:54

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