Materials and shells

These examples demonstrate fluid, solid-elastic, and layered spheres. All contrasts are relative to the exterior fluid. The example values are illustrative, not calibration specifications.

Fluid and gas interiors

using AcousticScattering

body = Sphere(0.01)
sound_speed = 1477.4
wavenumber = 2pi * 38000.0 / sound_speed
water_like = FluidFilled(1028.9 / 1026.8, 1480.3 / sound_speed)
gas_like = GasFilled(1.2 / 1026.8, 343.0 / sound_speed)
water_strength = target_strength(modal(body, water_like, wavenumber))
gas_strength = target_strength(modal(body, gas_like, wavenumber))
@assert isapprox(water_strength, -94.278687; atol = 1e-3)
(water_like = water_strength, gas_like = gas_strength)

(water_like = -94.27868652509476, gas_like = -44.988078917284966)

GasFilled aliases FluidFilled: both impose pressure and normal-velocity continuity. Gas resonances may require fine frequency sampling. A coarse grid can miss their peaks.

Solid elastic sphere

solid = SolidElastic(7800.0 / 1026.8, 5900.0 / sound_speed, 3200.0 / sound_speed)
solid_solution = modal(body, solid, wavenumber)
@assert isfinite(target_strength(solid_solution))
target_strength(solid_solution)

-50.74418414588774

Inputs are density, longitudinal-speed, and shear-speed contrasts. See Modal series for the elastic boundary conditions.

Fluid and elastic shells

fluid_shell = Shelled(FluidLayer(1.1, 1.05), VacuumInterior(), 0.9)
filled_shell = Shelled(FluidLayer(1.1, 1.05), FluidInterior(1.0, 1.0), 0.9)
elastic_shell = Shelled(ElasticLayer(7.8, 4.0, 2.0), FluidInterior(1.0, 1.0), 0.9)
shell_strengths = [target_strength(modal(body, configuration, wavenumber))
    for configuration in (fluid_shell, filled_shell, elastic_shell)]
@assert all(isfinite, shell_strengths)
shell_strengths

3-element Vector{Float64}:
 -45.82177800601859
 -97.87196109022403
 -45.60115186444555

0.9 is inner radius divided by outer radius. The Sphere radius is the outer radius. VacuumInterior() imposes pressure release at the inner fluid-layer surface. It is not a zero-density FluidInterior.

Viscous flesh and an elastic wall

flesh = ViscousLayer(sound_speed, 1.05, 1.02, 1e-5, 1e-6)
wall = ElasticLayer(1.1, 1.2, 0.2)
layers = LayeredMaterial(flesh, wall, 0.8)
swimbladder = Shelled(layers, FluidInterior(0.0012, 0.23), 0.7)
low_wavenumber = 2pi * 1000.0 / sound_speed
viscous_solution = modal(body, swimbladder, low_wavenumber; m_max = 0)
@assert isfinite(target_strength(viscous_solution))
target_strength(viscous_solution)

-79.09785446777451

Both ratios use the outer body radius. The gas core ends at 0.7 * radius, and the elastic wall ends at 0.8 * radius. Viscosity inputs are kinematic viscosities in m²/s. The implemented model is restricted to the monopole (m_max = 0). Higher orders are not supported.

Structural shell FEM instead uses Shelled(poisson, density, youngs_modulus) with Shell(body, thickness). See FEM and shell coupling for its absolute units and distinct interior-fluid arguments.