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ESSMS

Source: vignettes/essms/index.Rmd
index.Rmd

Overview

Unvalidated
Theory Implementation

These pages are grounded in the classical elastic-shell scattering literature for fluid-filled spherical shells (Goodman and Stern 1962; Faran 1951; Stanton 1990).

The elastic shelled spherical modal series (ESSMS) is the package’s layered spherical family for an elastic shell surrounding either a fluid interior or a pressure-release cavity.

Core idea

Represent the exterior acoustic field, the shell’s longitudinal and transverse elastic fields, and the interior acoustic field in spherical modes, then match pressure, displacement, and traction conditions at both shell interfaces.

Best for

  • Spherical elastic shells with fluid or gas interiors
  • Layered shell problems where shell resonances matter explicitly
  • Theoretical reference work on spherical shell scattering

Supports

  • ESS spherical geometries
  • Exterior seawater (medium 1), shell (medium 2), and interior fluid or cavity (medium 3)
  • Pressure-release and fluid-filled shell interiors

Main assumptions

  • Perfectly spherical shell geometry
  • Homogeneous isotropic shell material
  • Linear elasticity and linear acoustics
  • Modal truncation of an exact spherical layered system

Validation status

  • The package does not yet claim external validation across the current public scope.

Family pages

  • Implementation: current usage and validation status
  • Theory: full layered shell derivation, tractions, and mode-wise boundary systems

References

Faran, James J. 1951. “Sound Scattering by Solid Cylinders and Spheres.” The Journal of the Acoustical Society of America 23 (4): 405–18. https://doi.org/10.1121/1.1906780.
Goodman, Ralph R., and Raya Stern. 1962. “Reflection and Transmission of Sound by Elastic Spherical Shells.” The Journal of the Acoustical Society of America 34 (3): 338–44. https://doi.org/10.1121/1.1928120.
Stanton, T. K. 1990. “Sound Scattering by Spherical and Elongated Shelled Bodies.” The Journal of the Acoustical Society of America 88 (3): 1619–33. https://doi.org/10.1121/1.400321.