Figure 20. (a,b) Frequency responses of all periodic solution branches in Case E (Table 1) when the base acceleration is 12 m/s 2 . Refer to Table 2 for branch categorization. (a,b) Show sweep responses, stroboscopic points, and HBA solutions of Beam 1 and Beam 2, respectively. Unstable HBA solutions are suppressed in the figure for simplicity. (c,d) HBA results of Branch D and Branch F as the base acceleration increases. The base accelerations are 16, 18, and 19 m/s 2 . (c,d) Show Branch D and Branch F are connected when the base acceleration is 19 m/s 2 . Stable and unstable HBA solutions are plotted by the solid line and dot-dashed line, respectively. The triangle markers indicate the bifurcation points as follow: sn saddle-node Figure 20a,b show frequency responses of all periodic oscillation branches in Case E (beam length ratio = 0.971) solved by the proposed HBA when the base acceleration is 12 m/s 2 . In the first primary resonance, a route, from Branch A to Branch D with a discontinuous jump, is not observed. In this regard, because the interwell motion is overlooked in the first primary resonance if frequency sweep algorithm is employed along the intrawell motion in Case E, an HBA is required to reveal the interwell dynamics. In the second primary resonance, Branch E, interwell motion branch, is separated from Branch C as demonstrated previously in Fig. 16, and the stability analysis confirms that Branch E is unstable across the entire frequency range. Instead, the only conspicuous branch is Branch F which belongs to Zone C in Fig. 11. Although Branch I, period—2 T asymmetri-