CA05 exercise · Radiation and BEM-preparation exercise
Discretise a baffled vibrating plate into constant-velocity patches, evaluate a Rayleigh-integral pressure estimate and interpret radiation indicators such as coincidence frequency.
Aim
This exercise connects structural velocity from CA04 to acoustic radiation in CA05. You approximate a vibrating plate by small patches and sum their Rayleigh-integral contributions at receiver points.
BEM and Rayleigh-integral models do not mesh the full exterior air volume. Instead, they use boundary or surface data, such as normal velocity, to evaluate radiated pressure.
Which input is most directly used by the Rayleigh integral for a baffled vibrating plate?
For a 1.0 m × 0.6 m plate discretised by 20 × 12 patches, compute the area of one patch. For an aluminium plate with h = 3 mm, estimate the coincidence frequency.
Python exercise
The Python code discretises the plate into patches and plots the pressure field in a plane above the plate.
Expected observation
The pressure field should be strongest above the vibrating plate and show spatial variation due to interference between patch contributions.
Teaching note
This is a teaching-level radiation calculation. A production BEM model requires singular integration, proper boundary conditions and validation.
Written submission
Vibration versus radiation
Why can a structure vibrate strongly but radiate weakly?
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