Abstract
In this research the Rayleigh method was used to estimate the natural frequency of elliptical cross-sectional pipe where the major axis (2a) and the minor axis (2b) conveyed water containing nano-particles of Al2O3 at the ratio of volume concentration (Φ% = 0, 0.1, 03, 0.5). The study examined different boundary conditions (clamped – clamped, clamped – pin, clamped – free and pin – pin ). The ratios were firstly b/a=1, 2, 3, 4, 5 and then a/b=1, 2, 3, 4, 5 for different thickness “t” (1mm, 2mm), where the half major axis “a” (1cm, 2cm ) and the half minor axis “b” (1cm, 2cm) at the length of pipe “L” (1m), and using various pipe materials (PVC, aluminum and steel). This study predicted the natural frequency (ωn) and critical velocity (VC) which in the first case was larger than that at the second case for any construction of pipe. The natural frequency decreased slightly with the increase in the ratio (Φ% ). Finally, the natural frequency and the critical velocity were changed directly with increase of the ratio (b/a) while the inverse changes occurred with the increase of the ratio ( a/b) for PVC pipe but increased little for aluminum and steel pipes, due to different physical properties. Results have been compared with published theoretical and experimental results and found to conform.
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