Abstract:
The estimation of flexural wave intensity requires a knowledge of the internal forces present within the material, and these may be related to the spatial derivatives of displacement through the use of simple bending theories. A fundamental problem of intensity measurement lies in the estimation of these spatial derivatives. Commonly a finite difference approximation is used, however alternative techniques based on the decomposition of the motion into wave components can offer improved versatility and accuracy, along with greater insight into the dynamics of the system. These techniques are the subject of this thesis.
Wave decomposition is used to facilitate the estimation of flexural wave intensity in a beam, both in the far field and in regions where one and two near-fields exist. Different arrangements of transducers are compared in terms of the conditioning of the problem of estimating wave amplitudes from measured variables. It is shown that the choice of measured variables has an effect on the conditioning, and this is verified experimentally.
Wave-based techniques for far field plate intensity measurements, both using the commonly used assumption of one-dimensional propagation and assuming two-dimensional propagation, are investigated. A new technique is proposed in which it is assumed that the displacement of the plate can be expressed as the sum of plane waves, and that the wave amplitudes are a function of propagation direction which is approximated to a truncated complex Fourier series. The intensity can then be written in terms of the Fourier series coefficients. The effect that the use of different measurement systems has on the conditioning of the evaluation of the coefficients is discussed. Results of experimental measurements using the proposed techniques are presented.
