Numerical models for problems of acoustic scattering by thin elastic shells immersed in fluids

Area of Science:

• Acoustics
• Materials Science
• Computational Mechanics

Background:

• Acoustic scattering by elastic shells is crucial in underwater acoustics and material analysis.
• Accurate numerical modeling of these phenomena is computationally intensive.
• Existing models often require significant simplifications or high computational cost.

Purpose of the Study:

• To develop simplified yet accurate formulations for acoustic scattering by flooded and hollow elastic shells.
• To create a basis for efficient numerical models of elastic shell acoustics.
• To reduce complex fluid-structure interaction problems to boundary value problems.

Main Methods:

• Reduced the rigorous Helmholtz and Navier equations to a boundary value problem for Helmholtz equations.
• Utilized first-order expansion of elastic quantities about the shell's midsurface.
• Applied the boundary element method for numerical solutions.

Main Results:

• Developed simplified first-order models for acoustic scattering by elastic shells.
• Demonstrated that these models effectively capture elastic effects.
• Numerical solutions accurately reproduced low-frequency resonant peaks and dips for spherical shells.

Conclusions:

• The proposed simplified formulations provide an efficient basis for numerical acoustic scattering models.
• First-order approximations offer a good balance between accuracy and computational efficiency.
• The models are validated by comparison with exact solutions for spherical shells.