## Noise from stochastically excited structures: Modelling the noise from marine propellers excited by a turbulent boundary layer

##### Summary

People do not always realise sound is of great importance underwater. Marine life is
strongly affected by underwater noise. The source of underwater noise this work focusses
on is that of non-cavitating marine propellers. This noise is caused by pressure fluctuations
on the propeller, which arise because of the turbulent inflow generated by the ship
wakefield and hull, and the turbulent boundary layer on the blade. These fluctuations
are so complicated, that they are basically random but with known statistical properties.
Therefore, we need a stochastic approach to calculate the radiated noise. We need to first
calculate the response to this stochastic excitation and consequently the radiated noise.
To this end, we first show that we can calculate the response of a multi-degree-offreedom system under stochastic excitation. We demonstrate that we can calculate the
response of proportionally damped linear systems through a modal approach. A modal
approach is a valid approach, because the resonances of a system dominate the response.
Apart from this, we also show that we can calculate the response through modal analysis
for non-proportionally damped systems. This approach uses state-space to allow for modal
analysis.
These multi-degree-of-freedom systems are the basis of further calculations on real
geometries. The finite element method is employed to calculate the response of systems
with arbitrary geometries. A finite element system behaves largely in the same way as a
multi-degree-of-freedom system. We show that we can calculate the response of both the
proportionally and non-proportionally damped systems. These calculations are verified
for very simple systems by using analytical computations. One limitation of the nonproportional finite element method is that a point loading seems to give deviating results
for COMSOL Multiphysics and our state-space approach. However, this is not a large
limitation, as real world applications mostly use surface loads. Also, this difference does
not arise for proportionally damped systems.
Finally, to calculate the radiated noise of a system, we show that we can use structuralacoustic coupled systems. A modal analysis using the state-space approach, allows us to
calculate the response of the structure, and the pressure response in the fluid. Integrating
the cross-spectra of these responses at the interface gives the radiated sound intensity
spectrum. It turns out however, that the resulting pressure and structural response are not
the same for our calculations and the one done by COMSOL Multiphysics. Especially for
high density fluids (such as water), the results deviate significantly.
Further research into this topic should focus on finding an explanation for this
difference, for example by using an open-source software package to calculate system
matrices, or by finding the system matrices of a simple system by oneself, using the (semianalytical) expressions for a simple system. Experimentally verifying the results would
bring this part of the research to a close. Additionally, more research on characterising the
pressure spectrum caused by the inflow turbulence and turbulent boundary layer on a
marine propeller would make the calculations relevant for real-world applications.