Approximate high-order dynamic theory of a fluid layer in between two thick solids

Area of Science:

• Fluid dynamics
• Acoustics
• Solid mechanics

Background:

• Standard methods for fluid-coupled solids involve complex propagator matrix expansions.
• Analyzing fluid-solid interactions often requires high-dimensional models, increasing computational cost.
• Existing models may not accurately capture behavior at low frequencies or near resonances.

Purpose of the Study:

• To derive novel impedance boundary conditions (IBC) for thin fluid layers between solids.
• To develop a simplified, low-frequency model for fluid-coupled systems.
• To reduce the dimensionality of computational models for fluid-solid interactions.

Main Methods:

• Asymptotic integration of 3D fluid dynamics equations and boundary conditions.
• Neglecting vortex and viscosity effects for a thin fluid layer.
• Deriving recurrent relations for displacements and pressure components.
• Applying results to derive IBC with high-order asymptotic accuracy.

Main Results:

• Recurrent relations enable simple calculation of high-order displacement and pressure components.
• Novel impedance boundary conditions (IBC) derived with up to tenth-order asymptotic error.
• Validated IBC applicability until the first quasi-resonance frequency.
• Demonstrated validity for low-frequency, not just long-wave, analysis.

Conclusions:

• The derived IBC effectively simplify the analysis of fluid-coupled solid systems.
• These IBC offer a significant reduction in model dimensionality for practical applications.
• The method is robust within a reasonable low-frequency range, enhancing computational efficiency.