THEORETICAL STUDY ON PIPE OF TAPERED THICKNESS WITH AN INTERNAL FLOW TO ESTIMATE NATURAL FREQUENCY

This research study the effect of tapered thickness on the free transverse vibration of clamped ? free pipe which have uniform circular cross section conveying water by using Raighly ?Ritz method in the two case, the first involves the pipe have a constant wall thickness (t1) at clamped end equal to (1mm & 2mm) while the thickness (t2) at free end changes according to the ratio (t2/t1=0.2, 0.4, 0.6, 0.8, 1). In the second case the thickness at free end (t2) is constant (1mm & 2mm) whereas the thickness at clamped end (t1) changes at ratio (t1/t2=0.2, 0.4, 0.6, 0.8, 1). The pipe has a constant inner radius (Ri) of (1 cm or 2 cm) and different values of length (1m & 2m). This study shows in the 1st case the critical velocity (Vc) of the fluid can be decreased at the increase in length of the pipe at the same values of Ri & t1 but the value of critical velocity is increased with increasing t1, Ri and the thickness ratio (t2/t1) at the same length of the pipe. In addition at absence the flow of water the natural frequency of system is decreased with the increase in the ratio of thickness (t2/t1) and length of pipe, whereas Ri and t1 are decreased.