Asymptotic derivation of low-frequency models for fluid-loaded elastic plates

Shamsi, Shaharyaar Salman

Abstract

This thesis is concerned with asymptotic analysis of the low-frequency vibrations for fluid-loaded elastic plates. This involves examining a plane problem of an elastic layer under both two-sided and one-sided fluid loading.
The bending vibrations of an elastic layer immersed in a compressible fluid are studied, yielding the dispersion relation involving a fluid-borne bending wave supported by a special scaling. Following this, the four-term expansion is obtained and a comparative analysis with well-known thin plate formulations is provided.
A hierarchy of asymptotic models governing low-frequency in-plane motion of a fluidloaded elastic layer is established, assuming, apparently, for the first time, full contact conditions along the fluid-solid interface. Previously, the fluid loading was usually treated as a given stress prescribed along the surface of the layer within a Neumann-type boundaryvalue problem. This analysis demonstrated that both elastic stiffness of the layer and fluid inertia enter at leading order, whereas the transverse inertia of the layer appears at first order. Fluid compressibility and elastic rotary inertia appear at third order, while transverse shear deformation and the refinement of the conventional impenetrability condition come at second order.
The special case of the so-called light fluid loading is also studied, showing that the transverse plate inertia now appears at leading order, whereas other corrections appear at next order.
Extensional motions of a fluid-loaded layer are considered, taking into account the transverse compression of the plate. In this case, the radiation into the fluid results in complexvalued terms in the analysed dispersion relation.
Finally, forced time-harmonic vibrations are examined. The validity of the approximate formulation involving the Kirchhoff theory for plate bending is investigated, demonstrating that the aforementioned theory does not predict the effect of the plate stiffness on the radiation. Instead, a consistent approximation incorporating transverse compression is derived.

Citation

Shamsi, S. S. (2025). Asymptotic derivation of low-frequency models for fluid-loaded elastic plates. (Thesis). Keele University. https://keele-repository.worktribe.com/output/1369930

• Thesis Type: Thesis
• Online Publication Date: Aug 21, 2025
• Deposit Date: Aug 21, 2025
• Publicly Available Date: Aug 21, 2025
• Public URL: https://keele-repository.worktribe.com/output/1369930
• Award Date: 2025-08