Document Type : Research Note
Authors
1
Faculty of Engineering Shahid Chamran Univers
2
Faculty of Engineering Islamic Azad Universit
Abstract
Guided waves, due to their multimode characteristics, can be employed in NDT\&E, if suitable modes are selected. To show how suitable modes are determined, two elastic cylindrical models; a solid aluminum rod and a stainless steel pipe, are investigated, and longitudinal modes, which are axi- symmetric and, hence, find more applications in NDT, are studied in detail. A computer program is developed to extract real roots of the frequency equation and, then, to plot the frequency spectrum and dispersion curves of phase and group velocities and wave structures. These curves show the change in speed of propagation of the various modes if frequency changes. Wave structure curves can be used to identify the proper location of transducers to receive clearer signals. These curves also reveal a clear scope of particle motion on the boundary and inside the body of the cylinders, which could be used in theoretical and experimental result evaluations.For the solid aluminum rod, the cut-off frequencies of some modes are directly calculated and compared to similar values obtained from other sources. Close agreement indicates an acceptable level of accuracy. At high frequency-low wave length range, the phase velocity of the first mode converges to the velocity of the Rayleigh surface waves in aluminum, while, for the higher modes, this velocity converges to the shear wave velocity. Wave structure curves for some modes at specified frequencies indicate that the axial component of displacement near the surface and at the center of the rod is much higher than the radial component. Therefore, if such modes are to be used in tests, it is recommended to place the receiver at the cross section of the bar. For the stainless steel pipe with infinite length, study of the frequency spectrum, phase and group velocity curves shows similar trends as for the solid rod. From the wave structure curves for the first mode at two different frequencies, it is evident that the axial component of displacement, which is quite sensible on the inner and outer surfaces at lower frequency, vanishes on the outer surface at higher frequency, while the relative magnitude of the radial component remains the same, approximately, either at lower or higher frequencies. This phenomenon is also observed for the third mode, although the radial component on the inner and outer surfaces has higher resolution at higher frequencies than at lower ones. These studies can be employed for power lost optimization in pipes containing liquid (power leak) and for defect detecting in pipe thickness.
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