Dynamic Behavior of Axially Functionally Graded Pipes Conveying Fluid

Table 5

The variation of the second 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	61.5004	69.4713	74.6411	84.2515	92.8974	101.469	110.495	114.810
		0.50	61.5004	64.4750	66.6003	70.6875	74.4028	78.0533	81.7840	83.5138
		1.00	61.5004	61.5004	61.5004	61.5004	61.5004	61.5004	61.5004	61.5004
		2.00	61.5004	59.8213	58.4126	55.3901	52.5094	49.6838	46.9156	45.7453
		4.00	61.5004	58.9166	56.6441	51.4604	46.2746	41.1824	36.2901	34.2703
2.0	0.672	0.25	61.5959	69.5577	74.7221	84.3233	92.9617	101.527	110.547	114.860
		0.50	61.5959	64.5668	66.6895	70.7715	74.4821	78.1281	81.8547	83.5830
		1.00	61.5959	61.5959	61.5959	61.5959	61.5959	61.5959	61.5959	61.5959
		2.00	61.5959	59.9190	58.5124	55.4955	52.6216	49.8040	47.0441	45.8770
		4.00	61.5959	59.0156	56.7467	51.5737	46.4032	41.3315	36.4620	34.4515
3.0	0.587	0.25	61.6276	69.5864	74.7490	84.3471	92.9830	101.546	110.564	114.876
		0.50	61.6276	64.5973	66.7191	70.7995	74.5085	78.1529	81.8782	83.6060
		1.00	61.6276	61.6276	61.6276	61.6276	61.6276	61.6276	61.6276	61.6276
		2.00	61.6276	59.9515	58.5456	55.5305	52.6589	49.8439	47.0868	45.9207
		4.00	61.6276	59.0485	56.7809	51.6114	46.4459	41.3809	36.5192	34.5117