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Make it thicker!
For illustration purposes I found two (blank) PCBs of differing thicknesses - one is (tinned) double sided 1.6mm thick and the other a 4 layer board (from an old project) that is 4.0mm thick. Both boards are approximately 300mm wide. Clamping both in the vice, I pulled...
(and what you can't see is that I'm pulling *much* harder on the 4.0mm board!)
And a picture tells a 1000 words...
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(I'm sure beam deflection formulae (https://en.wikipedia.org/wiki/Deflection_(engineering)) would yield a far superior scientific approach to deciding how thick a PCB you need, but you get the idea![]()
Essentially, the bending stiffness is proportional to board thickness raised to the square. And it's slightly increased by continuous power planes and copper pours.
For the said board size, a metallic frame might be appropriate.
Vibrations must be expected on a vehicle. At worst case hitting the self resonance frequency of your board...
Google "board stiffener". There are various ways to do this.