Dynamic Behavior of Axially Functionally Graded Pipes Conveying Fluid

Table 6

The variation of the third natural angular frequencies for different material distributions and mass ratios when flow velocity is 20 m/s, , , and .

(mm)
1.0	0.796	0.25	120.726	135.934	145.948	164.997	182.693	200.618	219.333	227.933
		0.50	120.726	126.374	130.466	138.522	146.073	153.635	161.360	164.876
		1.00	120.726	120.726	120.726	120.726	120.726	120.726	120.726	120.726
		2.00	120.726	117.564	114.895	109.017	103.185	97.3618	91.6997	89.3743
		4.00	120.726	115.872	111.598	101.632	91.1682	80.6355	70.6481	66.6398
2.0	0.672	0.25	120.822	136.020	146.028	165.068	182.757	200.677	219.386	227.984
		0.50	120.822	126.466	130.555	138.606	146.153	153.711	161.432	164.946
		1.00	120.822	120.822	120.822	120.822	120.822	120.822	120.822	120.822
		2.00	120.822	117.663	114.996	109.124	103.298	97.4820	91.8275	89.5047
		4.00	120.822	115.972	111.702	101.747	91.2969	80.7826	70.8185	66.8177
3.0	0.587	0.25	120.855	136.049	146.056	165.092	182.779	200.697	219.405	228.002
		0.50	120.855	126.498	130.586	138.635	146.180	153.737	161.457	164.970
		1.00	120.855	120.855	120.855	120.855	120.855	120.855	120.855	120.855
		2.00	120.855	117.697	115.031	109.160	103.336	97.5231	91.8713	89.5494
		4.00	120.855	116.006	111.738	101.786	91.3409	80.8330	70.8770	66.8789