Elastic plates and shells

The problem of inverse scattering where the scattering structure is unknown, and the physical properties are predicted from the measured echo when the target is insonified with known waveforms, is investigated in this thesis. The scattering structure studied is a submerged, evacuated, spherical elastic shell. The formulation of the echo is carried out using thin shell theory for low and middle frequency range, which basically assumes that shear stresses are negligible. The echo is characterized by the form function in the frequency domain, and the impulse response in the time domain. The results of this thesis show that when using a chirp signal with a 200-250kHz bandwidth as the incident waveform, both the material and size of the shell can be recovered. However, the exact thickness of the shell wall couldn't be extracted.

The problem investigated in this thesis is that of an infinite, fluid-loaded, elastic cylindrical shell with an inhomogeneity of finite length excited by an acoustic plane wave. Seven inhomogeneities are considered to examine the parameters that influence the scattering. A full numerical approach and an iterative approach are developed to solve the shell and acoustic equations of motion expressed in the wavenumber domain. The response Green's function in the spatial domain is obtained using the hybrid analytical numerical technique, while the far-field scattered pressure is obtained by applying the Stationary Phase approximation. An analytical approach for the special case of a concentrated ring is developed, and the results compared to those from the full numerical solution. The range of applicability of the iterative approach is also investigated. The results show that the scattering pattern is a function of the spectral contents of the inhomogeneity distribution, and that the inhomogeneity mass influenced both the scattering pattern, and the scattering level. From the results it was also noted that an oblique angle of incidence steered the main lobe of the scattering pattern in the direction of the incoming acoustic wave. It is also demonstrated that the concentrated ring is usually a poor model to represent inhomogeneity of finite length.

A method of analysis is presented which employs a two-dimensional
plate test to determine the dynamic modulus of elasticity and loss
factor of viscoelastic damping materials. This method is based on an
energy approach to the free vibration of plates. The results derived
from the two-dimensional plate test procedure are compared to values
from conventional beam tests. This comparison indicates that the
material properties determined from the plate test method are in good
agreement with values determined from the beam test method. Thus,
the dynamic modulus of elasticity and loss factor of viscoelastic
damping materials can be determined from either beam or plate tests
and these values can be used in the two-dimensional plate equations
to evaluate the effectiveness of the damping material. In light of
this study, it is suggested that beam tests be performed to derive
viscoelastic material properties because of the simplicity of the
beam test procedure compared to that of the plate test procedure.

An acoustic compliant coating is applied on a fluid-loaded structure to control the radiated pressure, by decoupling the fluid medium from the vibrating surface. In this thesis the problem of an infinite cylindrical shell immersed in a fluid and entirely covered with an acoustic compliant layer, excited either by a ring force or an incident acoustic plane wave is considered. To model this problem two different approaches are used. The first one, which is available in the literature, is based on multi-layer shell theory. In this approach the scalar and the vector potential formulation are used to solve for the response and the scattering from the cylinder. The second approach is based on modeling the compliant layer by a normally reacting impedance layer on the surface of the shell. The velocity response Green's function of the shell is found using the hybrid numerical/analytical method. Results for the radiated and scattered pressure from the shell are also presented. The advantage of this second approach is that it can be used to model complex coating geometries. The results obtained with both approaches are compared.