This study investigates the stability of collapsible channel flow with an infinitely long flexible wall modelled as an Euler–Bernoulli beam, where wall tension, mass, damping and bending stiffness are incorporated. Specifically, we analyse the hydrodynamic Tollmien–Schlichting (TS) mode and flow-induced surface instabilities, including the travelling wave flutter (TWF) and static divergence (SD) modes, under both undamped and damped wall conditions. Our numerical results show that the TS mode exhibits a consistent insensitivity to bending stiffness across these two wall conditions. In the undamped system, bending stiffness effectively stabilises the TWF mode, and the divergent sensitivities of the TS and TWF modes to bending stiffness further induce TWFTS modal interaction within specific ranges of bending stiffness. In the damped system, bending stiffness similarly stabilises the SD mode and ultimately suppresses this mode at extremely high bending stiffness values. Notably, bending stiffness exerts a negligible influence on modal interactions under damped conditions, whereas wall mass acts as the primary driver of TWF-SD modal interaction in such cases. This work thus demonstrates that rational selection of flexible wall properties enables effective control over the onset of distinct instability modes, and thereby establishes a theoretical basis for the design of wall properties to actively regulate undesirable instabilities of collapsible channel flow in various applications.
Wang et al. (Thu,) studied this question.