Measurement of vibrational wave characteristics of beams and pipes with and without discontinuity
Control of undesirable transmission of noise and vibration along fluid filled pipes demands knowledge of the wave propagation characteristics. Because such waves are dispersive and wave reflection may occur at discontinuities, cross correlation and cross spectral methods of experimental determination of wave propagation characteristics, and of reflection and transmission coefficiences of discontinuities, are not effective. The thesis shows that a simple time or frequency analysis is not suitable for the determination of both dispersion and amplitude information, becasue the dispersion relation appears in the mathematical expression of the correlation peaks, and consequently corrupts the results. On the other hand, it is demonstated that wave field analysis, involving frequency-wavenumber decomposition, is able to produce both the dispersion relation k() and the amplitude of waves travelling in both directions in any type of waveguide. This is achieved by generating a two dimensional transfer function which is shown to vanish for wavenumbers of different value form the ratio /c(), and for values of k() = /c() displays Dirac peaks, the magnitudes of which are equal to the amplitude of the wave of corresponding wavenumber, and from which the dispersion relation is obtained. Using such a technique of wavenumber analysis, it is shown that it is possible to measure the complex reflection and transmission amplitude coefficients of a discontinuity in a waveguide. The important feature of this method, compared with simple time, or frequency, analysis consists in the fact that it can be applied to any kind of propagating dispersive wave, and no assumption has to be made about the expected dispersion relation involved. However, the application of this wavefield analysis to the measurement of reflection and transmission characteristics of a discontinuity is subject to some limitations which are investigated by using numerical simulation. With this technique, experimental results have been obtained for flexural waves in a rectangular cross-sectioned beam on which is fitted a mass-moment of inertia as a discontinuity, and comparison with theoretical results is presented. In addition, flexural waves in a piping system are investigated, and by using a similar technique, it has been possible to measure experimentally the dispersion relations of various flexural modes of different circumferential orders of a piping system when in-vacuo, and also when filled with liquid. An attempt to measure the reflection and transmission characteristics of a ring constraint fitted on the pipe when in-vacuo, and when fluid filled, is also reported with the associated difficulties which yield some proposition for further development of the technique in a view to future improvement.