Coupled frequencies of a rectangular hydroelastic system with two fluids

Comments on a class of orthogonality relations relevant to fluid-structure interaction

“…The modified ORs are thus almost identical to that used in [1,2]. For example [21,22], the eigenfunctions for the dissipative silencer shown in figure 2 (a) satisfy the OR:…”

“…The model problem and solution methods presented in the two articles are identical with the latter paper [2] offering more discussion but some of the same numerical results as the former [1]. In both articles the model problem is posed in terms of the fluid velocity potential.…”

“…The OR for the "drum-like" silencer [22,23] of figure 2 (b) is similar in structure: (18) in this case, of course, every occurrence of Y m (a) is replaced by Y m (d) since the membrane lies along y = d. Hydrodynamic applications that involve layered fluids [24,25] and submersed plates [26] have also been addressed. Interestingly, the article by Mohapatra et al [25] considers a boundary value problem which is very similar to that of [1,2] and uses the same OR. Further extensions include the development of the theory for wave propagation in 3D waveguides with flexible boundaries [27]- [28] and porous linings [29].…”

“…In two recent articles Amaouche and Meziani investigate the coupled frequencies of a hydroelastic system comprising two superposed fluids within a 2D container with one flexible wall [1,2]. The model problem and solution methods presented in the two articles are identical with the latter paper [2] offering more discussion but some of the same numerical results as the former [1].…”

“…. belongs to a well known class of non-Sturm-Liouville system for which ORs of the type presented in [1,2] are typical. As far as the author is aware, that presented in [3] does appear to be the first appearance in the literature of this class of OR.…”