Computation of acoustic scattering from elastic conical shells with endcaps using the hybrid finite element/ virtual source approach

Abstract

Studying and understanding acoustic scattering pattern from underwater targets has been of interest to various communities such as the archeologists and the navy for several reasons and applications. The present state-of-the-art technique in this area involves such methods as analytical approach and FEM/BEM numerical technique. This thesis aims to study and demonstrate the power of using the hybrid virtual source/FE approach where the physical presence of a target is replaced by virtual sources placed in the vicinity of the target and in a manner where the pressure/displacement relationship on the target surface is satisfied by the virtual sources when the target is being insonified. Accurate results for the far-field radiation of the target can be obtained by superposition of the point source Green's function of each virtual source. The hybrid virtual source/FE approach shows potential to be a computationally efficient method for computing acoustic scattering. The derivation of the dynamic flexibility matrix for an elastic conical shell with endcaps will be illustrated in this thesis. It will be shown that the dynamic flexibility matrix corresponds to the acoustic admittance matrix in the virtual source approach where the scattering functions are computed in the MIT's program OASES/SCATT.

(cont.) Moreover, the benchmarking and validation of the approach will be conducted with the hybrid analytical/ virtual source approach. Firstly, the approach predicts natural frequencies close to the theoretical analysis for higher order modes with more than 2 circumferential transverse vibration lobes. Secondly, it produces displacement profile that conforms to analytical results. The scattering functions are also in agreement those computed by the hybrid analytical/ virtual source approach, with discrepancies observed at lower frequencies. In exact terms, discrepancies start to appear for frequency in the range of 1000 to 2000 Hz for a 0.01m thick, 2 m long, 0.3m radius steel cylinder without endcaps. The scattering functions will be compared with the SCATT/OASES virtual source approach for pressure release and rigid cylinders and cones. For the hybrid FE/virtual source approach, the structural sound speed and density approach zero and infinity for pressure-release and rigid target respectively. On the other hand, in the SCATT/OASES virtual source approach, the pressure and displacement are required to vanish on the target surface respectively. It will be shown that the two approaches agree with each other.

(cont.) Moreover, scattering functions over steel cones and cylinders for various frequencies have also been derived in this research. The results will be interpreted physically and theoretically in this thesis. The importance of including structural damping in the finite element formulation of the target so as to reflect the effect of resonance on scattering will be illustrated. Other issues, such as effect of target orientations on scattering, will also be investigated in this thesis. The code has shown good potential for adaptation to compute scattering over other axisymmteric shapes using conical shells and circular plates as building blocks and the hybrid FE/ virtual source approach.