Dynamic Behavior of Axially Functionally Graded Pipes Conveying Fluid

Table 4

The variation of the first 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	22.1909	25.2702	27.1859	30.5936	33.4550	36.1690	39.0072	40.4687
		0.50	22.1909	23.3497	24.1498	25.6193	26.8588	28.0211	29.1967	29.7777
		1.00	22.1909	22.1909	22.1909	22.1909	22.1909	22.1909	22.1909	22.1909
		2.00	22.1909	21.5289	20.9829	19.8618	18.8849	17.9785	17.0936	16.6791
		4.00	22.1909	21.1690	20.2790	18.3220	16.5444	14.9059	13.3283	12.5955
2.0	0.672	0.25	22.3008	25.3695	27.2788	30.6755	33.5282	36.2347	39.0667	40.5260
		0.50	22.3008	23.4554	24.2525	25.7159	26.9498	28.1068	29.2778	29.8571
		1.00	22.3008	22.3008	22.3008	22.3008	22.3008	22.3008	22.3008	22.3008
		2.00	22.3008	21.6413	21.0977	19.9830	19.0138	18.1167	17.2418	16.8313
		4.00	22.3008	21.2828	20.3968	18.4519	16.6913	15.0763	13.5273	12.8067
3.0	0.587	0.25	22.3333	25.3989	27.3063	30.6998	33.5499	36.2543	39.0844	40.5430
		0.50	22.3333	23.4867	24.2829	25.7445	26.9767	28.1322	29.3018	29.8807
		1.00	22.3333	22.3333	22.3333	22.3333	22.3333	22.3333	22.3333	22.3333
		2.00	22.3333	21.6746	21.1317	20.0189	19.0520	18.1575	17.2856	16.8762
		4.00	22.3333	21.3165	20.4318	18.4904	16.7348	15.1266	13.5858	12.8688