Sweet Shooter:
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Given that nodes antinodes remain the same for one mass vs another, ei: frequency, Amplitude is to the largest extent the only variable and is affected by the force exerted upon it from the inside or the outside of the barrel. However frequency is a product of how much stress is resident or "built in" (like stretching a guitar string)... so bedding, up-pressure contributes to installing that. Therefore One influences the other.
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Ok, your may have a point. Please explain why all the mechanical engineering formulas for calculating barrel (or any other long shape such as a bar, solid rod or even an I or H beam) stiffness and resonant frequency do not include some outside force level or axis to make the barrel vibrate at different frequencies. If what you say is true, then all those formulas are bad.