Dependencies of (a) the quasi-mode periods (P) and (b) damping-time-to-period ratios (τ/P) on the ratio of the semi-major to semi-minor axis (a/b) for kink motions in a two-elliptic-tube configuration with the x-major orientation. The S​_x and A_x patterns are distinguished by the line styles. A number of dimensionless tube separations (d/b) are examined, as is differentiated by the different colors, with d/b constrained to avoid tube overlapping. All results pertain to a fixed combination of physical parameters, $[{\rho }_{\mathrm{i}}/{\rho }_{\mathrm{e}}=3,\overline{l}=0.4,kb=\pi /30]$. The horizontal lines represent the results for an isolated circular tube with the same set of parameters.