An approximate Green's function for a locally excited fluid-loaded thin elastic plate

Area of Science:

• Acoustics
• Mechanical Engineering
• Applied Mathematics

Background:

• Evaluating branch cut integrals is crucial for analyzing line-driven, fluid-loaded, thin elastic plates.
• Acoustic impedance in these systems involves a square root operator, complicating analysis.
• Previous work introduced complex layer analysis (CLA) for impedance approximation.

Purpose of the Study:

• To derive a rational function approximation (RFA) for acoustic impedance.
• To demonstrate the RFA's efficiency compared to CLA.
• To obtain an approximate Green's function for a line-driven plate.

Main Methods:

• Derived a rational function approximation (RFA) for acoustic impedance.
• Analyzed RFA accuracy in both Fourier and spatial domains.
• Utilized RFA to establish a differential relationship between plate surface pressure and velocity.
• Applied RFA with the plate's equation of motion to derive the Green's function.

Main Results:

• The RFA requires fewer terms than CLA for approximating acoustic impedance.
• The RFA was validated in both the Fourier and spatial domains.
• An approximate Green's function was derived, expressed as a sum of propagating and evanescent waves.
• Results showed reasonable agreement with numerical inversion of the exact integral.

Conclusions:

• The RFA provides a more efficient and accurate method for approximating acoustic impedance in thin elastic plates.
• The derived Green's function offers a valuable tool for analyzing wave propagation in such systems.
• This approach simplifies the classic treatment of line-driven, fluid-loaded plates.