Dynamic equations for fluid-loaded porous plates using approximate boundary conditions

Area of Science:

• Acoustics
• Solid Mechanics
• Materials Science

Background:

• Poroelastic materials exhibit complex behavior influenced by fluid flow within pores.
• Accurate modeling of thin, fluid-loaded poroelastic layers is crucial for applications in acoustics and structural engineering.
• Existing models may lack the precision or flexibility needed for diverse configurations.

Purpose of the Study:

• To systematically derive and present equations for fluid-loaded thin poroelastic layers under time-harmonic conditions.
• To develop a model based on Biot theory applicable to both open and closed pore systems.
• To validate the accuracy of the derived equations against established theories.

Main Methods:

• Application of Biot theory for modeling poroelasticity with open and closed pores.
• Utilizing series expansion techniques in the thickness variable.
• Formulating separate symmetric and antisymmetric plate equations with approximate boundary conditions.

Main Results:

• Derived asymptotically correct plate equations that can be truncated to arbitrary order.
• Presented analytical and numerical results for the developed theory.
• Demonstrated accurate prediction of plate behavior through comparisons with exact 3D theory and flexural plate theory.

Conclusions:

• The presented systematically derived equations provide an accurate method for analyzing fluid-loaded thin poroelastic layers.
• The model's flexibility allows for arbitrary truncation order, enhancing its applicability.
• The findings validate the effectiveness of Biot theory combined with series expansion for this class of problems.