Fig. 5.
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Displacement of tube axis at different longitudinal positions from simulations of modes n = 1 (top) and n = 2 (bottom). The solid and dotted lines represent oscillations with periods given by Eq. (20) for tubes of uniform density equal to ρi, 0 and ⟨ρi⟩, respectively. The dashed lines represent the exponential decay of the displacement of the fundamental mode.
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