Correction to: Method of experimentally identifying the complex mode shape of the self-excited oscillation of a cantilevered pipe conveying fluid

1 Correction to: Nonlinear Dyn https://doi.org/10.1007/s11071-022-07460-0

This correction stands to correct the original article, published with an error in Eq. 2 (Eq. 2) and errors in Figs. 3b, 9b and d, 10b and d, and 11b and d.

Fig. 3

Theoretical third complex mode shape of the pipe in the case that $\beta = 0.388$ and $\gamma = 74.2$ (a Real component of the mode and b imaginary component of the mode). Each mode shape is normalized by the absolute value $\sqrt {\Phi_{r}^{2} + \Phi_{i}^{2} }$ of the complex number $\Phi$ at the end point ($s = 1$)

Fig. 9

Comparison of experimental and theoretical mode shapes for Pipe 1: a and b shapes of the experimental real and imaginary modes and c and d shapes of the theoretical real and imaginary modes

Fig. 10

Comparison of the experimental mode shape with the theoretical mode shape for Pipe 2: a and b shapes of the experimental real and imaginary modes and c and d shapes of the theoretical real and imaginary modes

Fig. 11

Comparison of the experimental mode shape with the theoretical mode shape for Pipe 3: a and b shapes of the experimental real and imaginary modes and c and d shapes of the theoretical real and imaginary modes

The authors ask readers to consider the correct equation for Eq. 2 where, the first term, 3rd line from the end of equation 2, the error appears: $\int_{{0^{s} }} 1 /2v^{{*^{\prime}2}}ds$.

The correct notation for this part of the equation should be noted as: $\int_{0}^{s} \frac{1}{2} v^{{*^{\prime}2}}ds$.

Additionally, provided herein are revised figures: Figs. 3b, 9b and d, 10b and d, and 11b and d.

Noting these corrections, the original article has been corrected.