Interactions between sound and long partial enclosures

Abstract

This thesis aims at filling the missing research works in the current literatures concerning the field of sound and long partial enclosures. The first part of the thesis is to set up theoretical models for the internal sound field generated by a flush-mounted circular piston in an infinitely long and rigid rectangular duct with apertures such as side opening(s) and a slot. The apertures are modelled as vibrating air pistons. Simultaneous equations of the vibrating air piston velocities at these apertures are derived. The radiation impedance of a square air piston in terms of wave-number, piston size and aperture thickness is also derived. The leaky sound behaviour of an open slot at the duct wall has been modelled. The air in the slot is modelled as a linear array of air pistons, which oscillate under the action of the sound excitation. A theory is developed to model in details the asymmetric sound radiation from the slot. This results in the introduction of a complex wave-number which is used to model the sound propagation inside the leaky duct. The second part of the thesis demonstrates the finite element numerical modelling of leaky duct. In-duct modal decomposition technique is adopted to analyse the computed sound pressures. Contributions of discrete propagating modes are examined. Numerical results show excellent agreement with the predictions from the new mathematical model developed in the first part of this study. A method to predict the abovementioned complex wave-number for different slot dimensions is derived. The findings show that the complex wave-number correlates closely with the propagation constant and the slot length. The present research formulates the theoretical prediction of sound propagation phenomena along a leaky duct. This breakthrough generalizes current understanding on acoustical properties in tube-like cavity.