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The second issue is concerned with the real-valued loops on otherwise complex subsonic branches, involving the fluid mode increasing away from the plate.
The effect of surface tension is investigated in detail and it is found that for the parameter d̂ (=depth of fluid layer/depth of porous layer) very small, the surface tension has a strong effect on convection dominated by the porous medium, whereas for d̂ larger the surface tension effect is observed only with the fluid mode.
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The formulation is restricted to frequencies well below the cut-on of higher order fluid modes.
The theory developed applies below half the ring-frequency and when higher order fluid modes are cut off.
Rapid spatial variation in the velocity of the cochlear partition requires one to treat high-order fluid modes within the cochlear fluid.
Proper orthogonal decomposition is used to identify a small number of fluid modes to serve as the basis functions for the projections.
Natural frequencies of the plate coupled with sloshing fluid modes are calculated using Rayleigh Ritz method based on minimizing the Rayleigh quotient.
The proposed method is spectral, meshless and is based on the numerical evaluation of the covariance matrix associated with individual fluid modes.
By inspecting the low-frequency solutions of the dispersion equations corresponding to the different choices of fluid modes, a complete set of the flexural-type branches in an anisotropic fluid-loaded plate is identified.
Case (iii) produces an infinite sequence of progressively narrowing real-valued arches, whose upper arms rise up to cf and then transform into descending curves of solutions associated with the decreasing fluid modes (akin to the Sezawa continuum).
The first is related to the family of flexural-type branches (with origin at v= 0,k= 0), which evolve from the so-called A0 and A1 free-plate branches in a way that depends on the choice of fluid modes.
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