A Static Structural analysis has the pressure load that will stiffen the tube. How is the tube normally supported?

A simple support is to scope a Remote Displacement to the tube face and fix all six degrees of freedom. Make sure the Remote Displacement has the Behavior set to Deformable.

Drag a Modal analysis from the Toolbox and drop it on the Solution cell of the Static Structural analysis. That link will carry the stiffness increase from the pressure load into the modal analysis.