Vibroacoustics of complex structures - a wave chaos approach

Mohammed, Neekar Majeed (2021) Vibroacoustics of complex structures - a wave chaos approach. PhD thesis, University of Nottingham.

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Modelling vibro-acoustics is of crucial importance in many areas of mechanical engineering and industry. In this PhD thesis we develop theoretical and computational methods for modeling vibro-acoustics of mechanical structures. We focus on simple structures such as flat plates and thin shells to investigate the vibro-acoustic response of structures using a phase-space method. These simple structures will provide quantitative guidance to the analysis of the vibroacoustics response of complex structures.

In this thesis, an analytical model that captures wave effects using ray tracing treatment on thin shells is used. A ray dynamics describing wave transport on curved and smooth thin shells can be obtained from the underlying equations of motion via the Eikonal approximation. We first analyse mid-frequency effects near the ring frequency for thin shells consisting of a curved region smoothly connected to two flat plates. Using classical shell theory, we treat a corresponding ray-tracing limit derived in the short wavelength regime for bending, shear and pressure incident waves. We show that a smooth transition from total reflection to total transmission, along with the occurrence of resonant states, can be described in a ray tracing approximation by extending the treatment to complex rays. We are thus able to approximate the scattering matrix for waves incident on the bend accounting for tunnelling mediated by resonant states and uniformly treating the transition between the limits of totally reflected and totally transmitted waves.

A second contribution of this thesis is to propose a new method to model sound radiation using the vibrational response obtained from a phase space method such as the Dynamical Energy Analysis (DEA) method. The link between the structural response and the acoustic field can be achieved using so-called Wigner transform (WF) techniques. The energy density from a DEA structure-borne sound calculation can be related to field-field correlations of the vibrational displacement and then used to propagate the acoustic field using Rayleigh integral methods. In this way we compute the intensity of the sound pressure radiated from a flat plate. In addition to deriving an acoustic phase-space representation in the classical ray tracing limit, the impact of boundary conditions on acoustic radiation from vibrating flat plates, where the plate vibrations are assumed to be diffusive, has been studied. This technique has the potential to be used for generic complex mechanical structures.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Tanner, Gregor
Creagh, Stephen C
Keywords: vibro-acoustics, structural acoustics, vibrations, mechanical structures
Subjects: Q Science > QA Mathematics > QA299 Analysis
Q Science > QC Physics > QC220 Acoustics. Sound
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 65539
Depositing User: Mohammed, Neekar
Date Deposited: 04 Aug 2021 04:42
Last Modified: 04 Aug 2021 04:42

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