Elastic cylinder modal series solution

acousticTS implementation

Unvalidated Experimental

Overview Theory

These pages sit between the classical elastic-cylinder literature and later finite-length cylinder approximations used in fisheries acoustics (Faran 1951; Stanton 1988).

The elastic-cylinder modal-series solution is available through target_strength(..., model = "ecms"). The preferred geometry carrier is an elastic-cylinder ESS object, while the elastic material parameters are supplied through:

• density_body
• sound_speed_longitudinal_body
• sound_speed_transversal_body

The implementation check uses an independent direct transcription of the Faran-Stanton algebra rather than a package-to-package comparison. That is useful for confirming that the package code path reproduces the intended elastic-cylinder algebra on a shared grid, but it is not a substitute for an external benchmark ladder or a separate public software implementation.

ECMS is marked unvalidated because the check is an independent algebra transcription rather than an external benchmark ladder or separate public software implementation.

Reference case

The reference cylinder uses:

• length 40 mm
• radius 5 mm
• body density 2800 kg m^-3
• longitudinal speed 6398 m s^-1
• transverse speed 3122 m s^-1
• surrounding water density 1026.8 kg m^-3
• surrounding water sound speed 1477.3 m s^-1
• broadside incidence
• 12-200 kHz in 2 kHz steps

In acousticTS, the call is:

library(acousticTS)

elastic_cylinder <- fls_generate(
  shape = cylinder(
    length_body = 0.04,
    radius_body = 0.005,
    n_segments = 201
  ),
  density_body = 2800,
  sound_speed_body = 1500,
  theta_body = pi / 2
)

elastic_cylinder <- target_strength(
  elastic_cylinder,
  frequency = seq(12e3, 200e3, by = 2e3),
  model = "ecms",
  density_sw = 1026.8,
  sound_speed_sw = 1477.3,
  sound_speed_longitudinal_body = 6398,
  sound_speed_transversal_body = 3122
)

head(extract(elastic_cylinder, "model")$ECMS)

##   frequency        ka                       f_bs     sigma_bs        TS
## 1     12000 0.2551893 -0.001166938+1.400062e-05i 1.361941e-06 -58.65842
## 2     14000 0.2977208 -0.001556457+2.480975e-05i 2.423172e-06 -56.15616
## 3     16000 0.3402524 -0.001985893+4.061151e-05i 3.945421e-06 -54.03907
## 4     18000 0.3827839 -0.002447214+6.270084e-05i 5.992788e-06 -52.22371
## 5     20000 0.4253155 -0.002931593+9.261615e-05i 8.602815e-06 -50.65359
## 6     22000 0.4678470 -0.003429548+1.322009e-04i 1.177928e-05 -49.28881

Implementation check

Diagnostic	Value
Max abs. \Delta TS (dB)	0.00
Mean abs. \Delta TS (dB)	0.00
Frequency at max \Delta (kHz)	12.00
acousticTS elapsed (s)	0.08
Direct transcription elapsed (s)	0.03

This is not presented as a benchmark. It is an implementation identity check: the package output and the independent algebra transcription coincide on the shared grid, so the ECMS code path is reproducing the stated elastic-cylinder series rather than drifting numerically from it.

Spectrum overlay

Closing note

The point of this page is therefore narrower than the benchmarked modal-series families. ECMS is not being claimed here as externally validated. What is being documented is that the package reproduces the elastic-cylinder algebra it claims to implement, across a full frequency band rather than only at a few checkpoint frequencies.

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.

Stanton, T. K. 1988. “Sound Scattering by Cylinders of Finite Length. I. Fluid Cylinders.” The Journal of the Acoustical Society of America 83 (1): 55–63. https://doi.org/10.1121/1.396184.