Effect of shell axial deformation on flutter of cantilevered cylindrical shells under follower forces

Axial vibration effect of shell particles on dynamic stability of a cantilevered cylindrical shell under an axial follower force was addressed. In spite of free-ended shells, the reduced axial force under this effect cannot be derived analytically. Instead, an approximate method was proposed based on the fact that the static (and harmonic) axial deformation under an axial load in a free-ended beam are (almost) zero in a particular point near the middle of the beam, which was adopted as the equivalent fixed end of a cantilever. The work done by the nonconservative follower force was derived for a cantilevered beam and was extended to the case of a cantilevered cylindrical shell. The flutter load for a long free-ended shell was calculated using the equivalent cantilevered half-shell and compared with the previous results. Then, flutter load was calculated with and without the axial vibration effect for cantilevered shells with different lengths and thicknesses and the effect of each parameter was assessed on the flutter load and the critical circumferential mode number in each case.